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AN OUTLINE OF THE NECESSARY 

LAWS OF THOUGHT; 

A TREATISE ON PURE AND 
APPLIED LOGIC. 

BY WILLIAM THOMSON, M.A. 

FELLOW AND TUTOR OF gUEEN S COLLEGE, OXFORD. 
THIRD EDITION MUCH ENLARGED. 



js) , i^ gta 




LONDON: WILLIAM PICKERING. 
OXFORD: W. GRAHAM. 

'353- 






THE LIBRARY 

[Or C ONGR ESS 

WASHINOTOH 



KaXy [jLtv ovv kou Geioc, ev 1(t9i 9 y\ oo^yi, hv bg/uoig ett) 
tovq Xoyou$' eTjcvcov 3e aavTOv kou yvfjuvacai fxaXXov 5ia 
Trig ^0K0vaY\g <xx$vio-tov eIvou hdi kocXov/xsvyi; biro rcov ttoX- 
Xgjv a^oXsaxlag, kcog 'in vsog si' si Se /ay), ce %iot<pEu<zsTou 
y] aXv)9Eict> Plato. 



H 



TO 

SIR WILLIAM HAMILTON, Bart. 

PROFESSOR OF LOGIC AND METAPHYSICS IN THE 

UNIVERSITY OF EDINBURGH, 

ETC. ETC. 

THIS ESSAY 

IS BY HIS PERMISSION INSCRIBED. 



u 





PREFACE. 

?OME account of the exa£t pofition 
which this work pretends to occupy 
amidft a crowd of valuable treatifes on 
the fame fubjeft, may not be an unfit- 
ting introduction to its pages. The fyftem of Pure 
Logic or Analytic that has been univerfally accept- 
ed for centuries paft, is very defective as an in- 
ftrument for the analyfis of natural reafoning. Ar- 
guments that commend themfelves to any untaught 
mind as valid and praftically important, have no place 
in a fyftem that profefledly includes all reafoning 
whatever : and an attempt to reduce to its technical 
forms the firft few pages of any fcientific work, has 
generally ended in failure and difguft. The confe- 
quence has been that the more popular writers on 
Logic have begun to treat its ftridtly technical parts 
with a certain coynefs and referve. They have de- 
nied to the rules of the fyllogifm that prominent place 
once affigned to them, yet at the fame time they have 
refrained from rejecting as cumbrous and unneceflary 



vi PREFACE. 

an inftrument which did not fubferve any practical 
end in their fyftems. 

The prefent work is an attempt to enlarge the 
fcience of Pure Logic, fo that it may be adequate 
to the analyfis of any aft of reafoning. How far 
it has attained its obje£t ought to be decided by 
the application of its principles to many mifcel- 
laneous examples from different fciences ; and whilft 
I have rigoroufly and frequently applied this teft 
to it for ten years, I cannot hope that the par- 
tiality of an author will be a fufficient guarantee of 
its pretenfions, and therefore commend the fame line 
of examination to any one who believes, with me, 
that a fedulous pra&ice of logical analyfis will richly 
reward the underftanding with acceflions of ftrength 
and clearfightednefs. If the refult fhould be the de- 
tection of many errors and omiffions on the author's 
part, enough of matter may perhaps be left unfhaken, 
to prove that Pure Logic is not the mere officina ve- 
teramentaria — the warehoufe of ufelefs relics — it is 
too often taken for, but a practical fyftem — an im- 
portant branch of mental culture. 

To Sir William Hamilton, of Edinburgh, I am 
greatly indebted for valuable affiftance, freely and 
generoufly afforded, at the coft of much time and 
trouble. There is no longer any fear that fuch 
an acknowledgment will be mifconftrued into an ad- 
miffion that the prefent work only reports the opi- 
nions of that illuftrious philofopher ; as he has 



PREFACE. vii 

himfelf recognized its claim to an independent po- 
fition. # In truth, the extenfion of the fyllogifm, 
the enlarged lift of immediate inferences, the doc- 
trine of the three afpe£ts of propofitions, in Ex- 
tenfion, Intenfion, and Denomination, and the 
grounds for rejecting the fourth Figure of Syllogifm, 
which ferve, with other things, to give this little 
book its chara&er, were worked out originally with- 
out affiftance from any living author, from fuch ma- 
terials as any ftudent might command ; and it may 
perhaps be permitted me, without feeming to court a 
damaging comparifon, to point out that the twelve 
affirmative modes of Syllogifm in each figure, which 
here replace the much more limited number of the 
old fyftem, are precifely thofe which Sir William Ha- 
milton has found it necefTary, on his own principles, 
to adopt. This will be an evidence to the reader that 
the alteration in queftion is not rafh and arbitrary. 

To Profeflbr De Morgan, who has put forth, be- 
fides many excellent Mathematical Books and EfTays, 
an elaborate and acute Treatife on Formal Logic, my 
beft acknowledgments are due for his kind and patient 
explanations of certain parts of his fyftem. Other 
obligations to him are notified in their proper places. 

In the prefent Edition, the Applied Logic has 
been re-written, and many additions made to the reft 
of the work. 

* Sir W. Hamilton's Difcuflions in Philofophy, p. 126. 



viii PREFACE. 

The Appendix on Indian Logic, by my friend Pro- 
feflbr Max Miiller, of Oxford, of whofe labours, 
German, Englilh, and Sanfkrit literature already per- 
ceive the ripe fruits, at an age when moft ftudents 
muft be content ftill to till and fow, is intended to 
call attention to the interefting refemblances between 
the Greek and Hindu fyftems, which have never 
yet received the confideration they deferve. 

W* T. 

Queen's College, Oxford. 
December 6, 1852. 



TABLE OF CONTENTS. 



Introduction. 



§ 


Page 


i . ProcefTes precede laws . 


1 


2. Origin of Logic ...... 


3 


3. Logic, pure and applied .... 


5 


4.. This diftin&ion defended .... 


7 


5. Pure Logic ....... 


• 9 


6. Logic a Science ...... 


■ 13 


.7. Unconfcioufnefs in art ..... 


16 


8. Logic a practical Science . . . 


. 18 


9. Logic defined ...... 


18 


10. Its limits ....... 


20 


n-15. Form and Matter ...... 


21 


16. Firft and Second Intentions .... 


. 30 


Language. 




17. Thought and Language .... 


33 


18. Language defined ...... 


34 


19. Language has four functions .... 


■ 34 


20. It aids analyfis ...... 


35 


21. Degrees of this power ...... 


37 


22. Speech the higheft language. Why ? 


4.0 


23-24. It records thoughts ..... 


42 


25. It fhortens thinking ..... 


45 



x CONTENTS. 

h 

26. It communicates thoughts 
26*. Ariftotle's view of words 

27. Speech not effential to thought 

28 Though figns may be . 

29 Origin of language .... 
30-31. Growth of language 

Introduction concluded. 
33-35. 'Logic is a priori . 

36. Twelve names of Logic 

37. Ufes and pretenfions of Logic 

38. Its practical value .... 

39. Neglect of its details . 

40. Which are fhortened, not fimplified 

41. Divifion of Logic 

42-44. Objections . " 

45. Method . . . 

46. Ufe of Logic . 



Part I. Conception. 

47. Cognitions in general . 

48. Intuitions and Conceptions . 

49. Formation of Conceptions 

50. Higher and Lower Conceptions 

51. Genus, Species, Individual . 

52. Marks or Attributes . 
5 3 . Extenfion and Intenfion 

54. Determination 

55. Privative Conceptions . 

56. Three powers of Conceptions 

57. Logical Divifion . 

58. Partition . 

59. Definition .... 



CONTENTS. 



XI 



§ 
60. 

61. 
62. 
63. 
64. 



Denomination . 

Privative Conceptions . 

Relative Conceptions . 

Abftracl and Concrete Reprefentations 

Nature of General Notions . 

65. Queftions about Conceptions 

66. Summary ..... 



Page 
117 
120 
122 
124 
125 

135 
138 



Part II. Judgment. 

67. Judgment defined . .... 143 

68. Do&rine of Relation in Judgment . . . 144 

69. The two Predicable-Clafles . . . . .146 

70. Definition explained . . . . . 153 

71. Sources of Definition 155 

Table of Definition . . . . . . 157 

72. Attribute 158 

73. Common View of Relation . . . . .158 

74. Doctrine of Quantity . . . . . .167 

75. Doctrine of Quality 169 

76. Doctrine of Modality . . . . . .170 

77. Diftribution of Terms in Judgments . . .171 

78. Table of all the Judgments . . . . .176 

79. The fame, according to Sir W. Hamilton . .177 

80. Import of Judgments. Extenfion and Intenlion. 

Naming . . 180 

81. Explicative and Ampliative Judgments . .185 



Part III. Syllogism. Reasoning 

82. Syllogifm ..... 

83. Immediate and Mediate Inference 

84. Oppofition, and its Inferences 

85. Converfion and its inferences 

86. Inference by Privative Conceptions 



191 
193 

195 
202 
205 



Xll 



CONTENTS. 



87. Inference by Added Determinants 

88. Inference by Complex Conceptions 

89. Inference by Interpretation . 

90. Inference by Disjunctive Judgments 

91. Inference by Sum of Predicates 

92. Concluding Remark 

93. Canon of Mediate Inference . 

94. Order of Premiffes 

95. The Three Figures 

96. Special Canons of the Figures 

97. The Fourth Figure 

98. The Unflgured Syllogifm 

99. Modes of Syllogifm 

100. Table of Modes . 

1 01. A Mode of Notation . 

102. Equivalent Syllogifms 

103. Sir W. Hamilton's Notation 

104. Euler's Notation 

105. Inference in Extenfion and Intenfion 

106. Conditional Syllogifms 

107. Disjunctive Syllogifms 

108. Complex Syllogifms. Sorites 

109. Dilemma .... 
no. Incomplete Syllogifms 
in. Profyllogifm and Epifyllogifm 



Part IV. Applied Logic. 

1 12. Province of Applied Logic 

113. Science ...... 

114. Criterion of Truth .... 

115. Induction and Deduction . 

116. Search for Caufes. Inductive Methods 

117. Anticipation ..... 



CONTENTS. 



Xlll 



§ 

118. 
119. 
120. 
121. 
122. 
123. 
124. 
125. 
126. 
127. 
128. 
129. 
130, 
131. 
132. 
133. 
134. 









Page 


Colligation. Definition . . . 304 


Complete and Incomplete Induction 






306 


Degrees of Belief . 






314 


Syllogifm, Deductive and Inductive 






317 


Employment of Defective Syllogifms 






320 


Syllogifms of Analogy 






327 


Syllogifms of Chance .... 






331 


Syllogifms of Clarification . 






343 


Nomenclature ..... 






345 


Sources of Principles . 






348 


Errors and Fallacies .... 






35i 


Dealing with Errors .... 






35i 


Method. Definition, and Divifion 






352 


Subordinate parts of a Science 






355 


Categories. ..... 






356 


Divifion of the Sciences 






360 


Conclufion .... 






363 



Appendix. On Indian Logic (by ProfefTor Max Miiller) 367 



ERRATA. 

P. 52. for prepojltions read proportions. 

P. 266. No. III. for that are B 9 read that are A, are B. 



OUTLINE OF THE LAWS OF 
THOUGHT. 

INTRODUCTION. 

El'Trcofxsv obv Si a QgaxEoov Tig r\ TrgoOeatg hou rig b 
vKQirog Tsaang Trig avofiwrimg iTrurTYifAYig. 

Alexander Aphrod. 




OUTLINE OF THE LAWS OF 



CORRECTIONS. 

P. 236, column 3, dele U O O 

P. 248, column $, for UOO, read U O rj 

for UwO, read U 10 w 



■laft line, for 15, read 16, and for 21, 20. 



P. 313, note, for tori, read Sloti. 



— ^^^> far from being neceffary to the procefs, 
that we cannot difcover what they are, except by 
analyfing the refults it has left us. Poems mull have 
been written before Horace could compofe an " Art 
of Poetry," which required the analyfis and judi- 
cious criticifm of works already in exiftence. Men 
poured out burning fpeeches and kindled their own 
emotions in the hearer's breaft, before an Art of 

B 



2 OUTLINE OF THE 

Rhetoric could be conftru£ted. They tilled the 
ground, eroded the river or the fea, healed their 
fickneffes with medicinal plants, before agriculture, 
chemiftry, navigation, and medicine, had become fci- 
ences. And wherever our knowledge of the laws of 
any procefs has become more complete and accurate ; 
as in aftronomy, by the fubftitution of the Coperni- 
can for the Ptolemaic fyftem ; in hiftory, by a wifer 
eftimate than our fathers had the means of forming, 
of modern civilization and its tendencies ; in che- 
miftry, by fuch difcoveries as the atomic theory and 
the wonders of eleitro-magnetifm ; our progrefs has 
been made, not by mere poring in the clofet over the 
rules already known, to revife and corre£t them by 
their own light, but by coming back again and again 
to the procefs as it went on in nature, to apply our 
rules to fa£b, and fee how far they contradicted or 
fell ftiort of explaining them. Aftronomers turned 
to the ftars, where the laws they fought for were 
day and night fulfilling themfelves before their eyes ; 
hiftorians collected fadts from the records of different 
countries, watched men of many races, of various 
climates, differently helped or hindered, for there, 
they knew, the true principles of ^hiftory were to be 
read ; and chemifts, in the laboratory, untwifted the 
very fibres of matter, and watched its every pulfe 
and change, to come at the laws which underlaid 



LAWS OF THOUGHT, 3 

them. " Even geometry," fays the great chemift, 
Juftus Liebig, " had its foundation laid in experi- 
ments and obfervations ; moft of its theorems had 
been ken in practical examples, before the fcience 
was eftablifhed by abftradr. reafoning. Thus, that 
the fquare of the hypothenufe of a right-angled tri- 
angle is equal to the fum of the fquares of the other 
two fides, was an experimental difcovery, or why 
did the difcoverer facrifice a hecatomb when he made 
out its proof? " * 

§ 2. The fame applies to Logic, or the fcience of 
the laws of thought. The procefs of thought, or that 
a£tive function of the mind by which impreffions re- 
ceived from within or from without are defcribed, 
claffified, and compared, commenced long before the 
rules to which it adheres with unfailing ftri£tnefs, 
had been drawn out. And though they do not de- 
pend on experience — u e. their truth may be tried 
and made manifeft without recurring to examples — ■ 
ftill without experience, without the power of watch- 
ing our own thoughts and thofe of others, there could 
never have been a fcience of Logic, which had its 
origin when fome refle&ive mind, that had for years 
performed the various afts of thought fpontaneoufly, 
began to lay down the laws on which they take 

* Chemical Letters, Second Series, p. 6. 



4 OUTLINE OF THE 

place, or to give rules for repeating them at pleafure. 
The cleareft reafoner cannot with propriety be called 
a logician, fo long as he difputes fpontaneoufly and 
without rule ; whilft the man of the humbleft rea- 
foning powers may lay claim to the title, in fo far as 
he reafons according to laws, afcertained by reflec- 
tion upon the procefs of thinking.* If, for example, 
we call Zeno of Elea the inventor of Dialectic or 
Logic in Greece,f it is not in virtue of his marvel- 

* See Coujin, Nouveaux Fragments, p. i, feq. 

f It is uncertain whether the Hindu work of Gotama, 
called Nyaya, is anterior to the Greek logical fyftem. An 
account of it is given in Colebrooke's Ejfays, vol. ii. The fimi- 
larity between the Hindu and Grecian fyftems will be appa- 
rent to all who are acquainted with the latter, from a glance 
at the following extra<5t from Colebrooke's account. " A re- 
gular argument or complete fyllogifm (Nyaya) confifts of five 
members or component parts $ ift, the proportion ; 2nd, the 
reafon 5 3rd, the initancej 4th, the application,- 5th, the con- 
clufion. Ex. 

1 . This hill is fiery ^ 

2. For it fmokes. 

3 . What fmokes is fiery ; as a culinary hearth. 

4. Accordingly, the hill is fmoking ; 

5. Therefore it is fiery. 

Some [commentators] confine the fyllogifm {Nyaya) to three 
members, either the three firft, or the three laft. In this latter 
form it is quite regular. The recital joined with the inftance 
is the major $ the application is the minor ; the conclufion fol- 
io ws." Vol. ii. p. 292. Alfo Coujin, Hiftoire, Lecon vi. and 
St. Hilaire, Logique cfAriJiote, ii, 330* 



LAWS OF THOUGHT. 5 

lous ingenuity in arguing againft the poffibility of 
motion, becaufe this might have been the refult of 
natural acutenefs ; but becaufe his arguments, all 
conftrucSted upon one type, that of forcing his anta- 
gonifts into an abfurd pofition by reafonings drawn 
from their own views, feem to indicate the pofTeffion 
of a logical rule, the fame which now has the name 
of reduclio ad abfurdum. He had refledted upon thofe 
modes of argument which his pofition led him to 
adopt fpontaneoufly, and had formed a general rule 
or plan which aflifted him in forming like arguments 
in future. Logic then, like Philofophy, of which it 
is a part, arifes from the reflection of the mind upon 
its own procefTes ; a logician is not one who thinks, 
but one who can declare how he thinks. This im- 
portant diftin£tion, which has been too often neglect- 
ed, muft govern all refearches into the hiftory of the 
fcience. 

§ 3. Logic has been defined to be the fcience of 
the neceffary laws of thought. But this definition, 
the correctnefs of which mail prefently be examined 
more particularly, requires a few words of general 
explanation. Our thoughts are formed indeed by 
laws ; and when we conceive, abftracT:, define, judge, 
and deduce, we put in practice fo many afcertainable 
principles. But does Logic fimply explain thefe laws 
in themfelveSy or contemplate them in their ufes^ as 



6 OUTLINE OF THE 

affifting and regulating our efforts in feeking after 
knowledge ? This diftin£tion is analogous to that 
which is drawn between Anatomy and Phyfiology, 
the former of which fimply examines what are the 
parts of the human frame, and the latter, the Science 
of Life, dwells upon the ufes and developments of 
the parts : the one declares that I have a brain, and 
the other determines that it is the principal feat of 
paffion, fenfation, and reafon ; and that it is weak in 
childhood, ftrong and conftant in mature life, and 
fubjeft to a gradual decay in age. It is competent 
to us unqueftionably to confider the principles of 
thought under this twofold afpe£t of their nature and 
their employment. Thus, if we take a judgment j 
fay, " The happinefs of the human family will in- 
creafe in proportion to the increafe of mutual love," 
and confider it in its own nature, we mail decide that 
it is a judgment correft in form, that certain other 
judgments may be gathered from it, that it has fome 
qualities which may belong to a judgment, and wants 
others ; and fo far we are only looking at the judg- 
ment in itfelf^ by what we know of the laws of 
judgment. But if we confider this example in con- 
nexion with truth and' knowledge, we are led to ex- 
amine further, whether it is falfe or true, whether in 
forming it we fulfilled thofe conditions, of obfervation 
and reafoning, without which we have no right to 



LAWS OF THOUGHT. 7 

expect a true refult; to what region of thought it 
belongs, and what is the method, be it teftimony, 
deduction from principles, or obfervation of facts, by 
which judgments are to be obtained in that region. 
In the former cafe we only put in requifition what 
may be called pure Logic, which is defined to be the 
fcience of the necejfary laws of thought in their own 
nature; whilft the queftions in the latter cafe belong 
to applied Logic, or the fcience of the necejfary lazvs 
of thought as employed in attaining truth. 

§ 4. But is this diftinction worth preferving in our 
expofition of the fcience ? Many logicians, believing 
that they muft undertake to teach men " the art of 
reafoning," do not attach any value to the laws of 
thinking, except in fo far as the employment of them 
may help men to think, and fo to enlarge their ftock 
of truth ; that is, they do not regard pure Logic as a 
diftincT: branch of their fubject. But there is one 
grand reafon for the oppofite courfe. Truth is a 
wide word, and denotes all that we can ever know 
of ourfelves, the univerfe, and the Creator. The 
fcience which explains how the mind deals with truth, 
muft be loofe and indefinite, as its object-matter is 
of infinite extent ; fo that applied Logic can never 
attain perfe£t completenefs and precifion, becaufe it 
can never affirm that it has fhown how the mind 
deals with every part of truth and knowledge. But 



8 OUTLINE OF THE 

the laws of thought themfelves are few in number, 
and lie, in examples of perpetual occurrence, under 
every thinking man's obfervation ; and therefore it 
may be declared with tolerable correftnefs when a 
full and accurate view of pure Logic has been taken. 
To fecure that which we have completely mattered, 
it is defirable to keep it feparate from that in which 
perfe£t completenefs is hopelefs ; and therefore we 
purpofe to confider Logic under two diftin6t lights, 
firft as a fcience of laws, and next as a fcience of 
laws applied to pradtice. 

But here a caution is neceflary (which we fliall 
have to repeat in connexion with the tripartite divi- 
fion of pure Logic itfelf ) that as the diftin&ion is in 
a meafure arbitrary, for the laws of thought are al- 
ways put in force with a view to the attainment or 
communication of knowledge, it will be impoffible 
to maintain it with perfedt confiftency throughout 
our labours. Occafions conftantly arife when the 
line of demarcation becomes blurred and confufed; 
when the bare laws of thought cannot be explained 
without the mention of that truth, in the fearch for 
which they are always employed: thus, in treating 
of Definition, which is one form of judgment, we 
imply the exiftence of a perfon/ir whom it is necef- 
fary to define a given notion that he may poflefs the 
true meaning of it, and be able to identify the things 






LAWS OF THOUGHT. 9 

for which it ftands. All that can be expefted from 
us is, that, even if we find it neceflary to repeat the 
fame truths in the two divifions, we do not defert our 
point of view, but explain the laws of thought, firft 
mainly for themfelves, and then mainly in relation to 
truth, which is the object of all thought and enquiry. 
§ 5. Pure Logic (which is later in the order of 
difcovery than applied, inafmuch as it is formed by 
abftra£ling from that more general fcience,) takes no 
account of the modes in which we collect the mate- 
rials of thought, fuch as Perception, Belief, Memory, 
Suggeftion, AfTociation of Ideas ; although thefe are 
all in one fenfe laws of thought.^ Prefuppofing the 



* " Now univerfal Logic is either pure or applied Logic. 
In the firft we make abftra£Kon of all empirical conditions, 
under which our underftanding is exercifed $ for example, of 
the influence of the fenfes — the play of the imagination — the 
laws of memory — the power of habit, of inclination, Sec. ; con- 
fequently alfo of the fources of prejudices, nay, in facl, in 
general, of all caufes out of which certain cognitions arife to 
us or are pretended to do fo, fmce they merely concern the 
underftanding under certain circumftances of its application, 
and in order to know them, experience is requifite." — Kanfs 
Critique, p. 58, Englifh Tranfl. ift Ed. The ground here 
taken is different from that in the text. I do not fay they are 
contingent , for memory, for example, enters into every acl: of 
thought ; but, that they are fubfidiary $ thought is not com- 
plete without them, but at the fame time thought is never 
complete with them alone. 



io OUTLINE OF THE 

pofleffion of the materials, it only refers them to 
their proper head or principle, as conceptions, as 
fubje&s or predicates, as judgments, or as arguments. 
It enounces the laws we muft obferve in thinking, 
but does not explain the fubfidiary procefles, fome or 
all of which muft take place to allow us to think. 
Metaphyfics is the fcience in which thefe find place ; 
but they alfo belong to applied Logic, becaufe they 
are fo many conditions under which the human mind 
acquires knowledge. Again, in pure Logic, the dif- 
ferent procefles of the mind are regarded in their 
perfect and complete ftate ; whilft in applied, the 
imperfe£t faculties of man, the limited opportunities 
of obfervation, the neceflity of deciding upon a quef- 
tion when the materials of a judgment are ftill inef- 
ficient, impofe many limitations on the perfection of 
our knowledge. Thus, whilft pure Logic only treats 
of arguments that are certain and irrefutable, the 
moft important duty of applied Logic is to determine 
under what conditions imperfedl arguments, fuch as 
the Example, the Imperfect Indu&ion, the Deduc- 
tion from a propofition that is not truly univerfal, and 
fome of the Rhetorical Enthymenes, can be fairly 
employed, and to fhow, that though thefe weaker 
forms are fo many deviations from a perfect demon- 
ftrative argument, they are fo far from fuperfeding 
the perfedt forms, that in reality each of them appeals 



LAWS OF THOUGHT. n 

to, and attefts the cogency of, fome perfect form, 
to which it ftrives, as it were, to conform itfelf. As 
we are anticipating, a very eafy example muft fuffice 
to illuftrate our meaning. Every one is perfectly 
certain of the truth of the proportion that men grow 
infirm and die; of which we have been convinced 
partly by our own experience of men, and partly by 
the experience of others, delivered to us from all 
quarters, in the fober pages of the moralift as well as 
in the recklefs lyrics of the reveller. Nor does our 
conviilion of this truth permit itfelf to be difturbed 
by the confideration, which is likewife undeniable, 
that the whole aggregate of this experience does not 
in itfelf warrant any ftatement having all mankind 
for its fubject : that even fuppofing the decadence 
and death of every man in times paft had been ob- 
ferved, which is utterly inconceivable, at any rate 
there are many now living upon whom the common 
doom has not paffed, and whofe cafes therefore can- 
not enter into the fum of our experience. In a word, 
we have concluded from an experience that many 
men have become infirm and died, the much wider 
truth that all men do fo ; and this is warrantable in 
the given cafe, and we are right in rejecting upon 
the faith of it an afiertion, unlefs fupported by evi- 
dence that tranfcends experience, that one man has 
not died, fuch as we have in the fable of the Wan- 



12 OUTLINE OF THE 

dering Jew, or a propofal to obviate death in future, 
fuch as was involved in the fearch of the alchemift 
for an Elixir of Life. But that this mode of argu- 
ment from a particular to a univerfal, from fome to 
#//, is not valid in itfelf, is evident from applying it 
to another cafe, in which it is abfurdly folk— fome 
men are tall^ therefore all men are tall : and the only 
form perfectly indifputable in itfelf would be, " the 
men whom we have obferved have all died, and thefe 
men are all men, that is, the only men, therefore all 
men die," which from the nature of this cafe cannot 
be employed. But applied Logic firft fhows that this 
perfect argument is the meafure of the validity of the 
other; that our conclufion is only true if we can 
fay, not indeed " thefe men are all men," which is 
impoffible,but the equally ^/z^n?/ proportion, " Thefe 
men are (as good as) all men;" thus conforming really 
to the perfectly conclufive argument ; and next, how 
and under what circumftances we can conform the 
incomplete to the complete enumeration, how fome 
can ever be faid to be as good as all for purpofes of 
argumentation. 

But it is time to proceed to examine the different 
parts of the definition of pure Logic, by fhewing that 
Logic is a fcience, rather than an art — that it is a 
fcience of the neceflary laws or forms of thought — 
that it has thought rather than language for its ade- 
quate objedt-matter. 



LAWS OF THOUGHT. 13 

§ 6. Logic is a fcience rather than an art. The 
diftinction between fcience and art is, that a fcience 
is a body of principles and deductions, to explain 
fome objeclr-matter: an art is a body of precepts^ 
with practical fkill, for the completion of fome work. 
A fcience teaches us to know, and an art to do y the 
former declares that fomething exifts, with the laws 
and caufes which belong to its exiftence, the latter 
teaches how fomething muft be produced.* An art 
will of courfe admit into its limits every thing which 
can conduce to the performance of its proper work ; 
it can recognize no other principle of felection. The 
painter may fail of perfect fuccefs from employing 
improper colouring materials, or a muddy and pe- 
rifhable varnifh, as well as from incorrect drawing 
or ill managed light and made ; the lower defect or 

* nsp; yivsnv ri^im, nspl to ov kirio^pti. Ariflotle. An, Poft. II. 
xix. 4. By fcience in the text is meant the fpe dilative fcience 
of Plato and Ariflotle ,• by Art the practical fcience. Plato 
feems to life fiyy* and Iti-ic-t^ as interchangeable terms {Theat, 
14.6, c). Again (Politicus, 258, D, E.) he divides hfie^ftat 
into irpattTutal and yvooa-rikccl ; the latter he would fubdivide (260, 
B.) into critical, which end in judging merely, and epitaclical, 
which lead us to fome praclical refult. See alfo Thetet. 202, D. 
Where Ariflotle diftinguifhes between Science and Art, which 
is not invariably the cafe, he explains them as we have done in 
the text, adding only that the object-matter of Science is ne- 
celfary or invariable 5 that of Art, contingent and variable. 
See An, Poft. 1, ii. Top, vi, viii. 1, Eth. Nic. vi. iii. 



14 OUTLINE OF THE 

the higher is fatal to that perfe& pi&ure which he 
wifhes to produce. So that an art may contain pre- 
cepts of a very diflimilar character ; the painter muft 
be taught Expreffion, Anatomy, and mixing of Co- 
lours ; the Rhetorician muft learn to manage his 
thoughts, his hearers, and his hands, with equal dex- 
terity. The fcience, on the other hand, having the 
obje£t-matter for its touch ftone, admits nothing ex- 
cept what relates direftly to it; and fo a far greater 
unity and fimplicity naturally belongs to it. Geome- 
try treats of nothing but the properties of fpace, be- 
caufe it is a pure fcience, whilft the arts founded 
upon it, fuch as Land-furveying, muft bring in fuch 
topics as inequalities of furface, ufe of inftruments, 
and the like. The fcience of Mufical Counterpoint 
teaches the theory of harmonic progreffions, and no- 
thing elfe ; but the mufician's art, in which it is em- 
ployed, muft add the knowledge of inftruments and 
their compafs, of the human voice, even fometimes 
of the powers of a particular finger. Now in the 
popular meaning of the word Logic, no doubt the 
notion of an art is more prominent ; to be able to 
reafon better, and to expofe errors in the reafoning of 
others, is fuppofed to be the obje£l of this ftudy.* 

* Upon the hiftorical view of the queftion, whether Logic 
is an Art or a Science, moft valuable remarks will be found in 
a paper by Sir William Hamilton, Edinburgh Review, 115, 
p. 202, feq. 



LAWS OF THOUGHT. 15 

But thofe writers who have followed out this view 
have been compelled to go over too wide a field for 
any one fyftem. Logic muft be the wideft of all arts 
or fciences ; becaufe thinking, which is its objecT> 
matter, belongs to all the reft ; it is ars artium^ the 
art which comprehends all others, becaufe its rules 
apply to every fubjecl: on which the human mind can 
be engaged. If then it is to be taught as an Art, it 
mould contain fpecific rules for reafoning or thinking 
in every region of thought ; it muft propofe to itfelf 
nothing lefs than to enable men of the moft various 
capacities to apply a fet of principles to effect the 
work of thinking correctly, under all circumftances. 
And the confequences are, an enormous expanfion 
in the firft inftance, from the huge mafs of heteroge- 
neous materials ; and a confcioufnefs of incomplete- 
nefs in the fecond, fince it is impoflible to fuppofe 
that fo vaft a work has ever been completely achieved. 
Works in which the attempt has been made often 
contain a chapter on Scriptural Interpretation, and 
perhaps another on Forming a Judgment on Books : 
— can it be fuppofed that the precepts under either of 
thefe heads can be complete ? The one is an epitome 
of all Theology, and the other, it might be faid, of 
all wifdom. Now Logic may be unqueftionably an 
art or a fcience ; but it feems that all we can do is 
to lay down the principles of the fcience and leave 



i6 OUTLINE OF THE 

each ftudent to form for himfelf his own art, to teach 
himfelf how to employ thefe principles in practice. 
In this way we may attain fomething like complete- 
nefs in a moderate compafs, and may efcape thofe in- 
ceflant ftiiftings of the boundaries of the art, which 
are inevitable where men have to fele£t a finite num- 
ber of precepts out of infinite knowledge. 

§ 7. Thofe who reprefent Logic as both art and 
fcience are accuftomed to affume that all arts, pof- 
felling the principles of correfpondent fciences, teach 
their application to practice, fo that art is but fcience 
turned to account. In the cafe of Logic this is not 
very far from the truth ; but as a general ftatement 
it is falfe, for it overlooks that notion of unconfciouf- 
nefs which is commonly involved in Art. Shak- 
fpeare is admitted to be a confummate artift, but no 
one means by this that his plays were compofed only 
to develope a certain exprefs theory of Dramatic 
Poetry, fuch as Coleridge, Horn, or Ulrici have fince 
founded upon them. No : the man of fcience pof- 
feffes principles, but the artift, not the lefs nobly 
gifted on that account, is poffefled and carried away 
by them. " The principles which Art involves^ 
fcience evolves. The truths on which the fuccefs of 
Art depends, lurk in the artift's mind in an undeve- 
loped ftate ; guiding his hand, ftimulating his inven- 
tion, balancing his judgment, but not appearing in 



LAWS OF THOUGHT. 17 

the form of enunciated propofitions." * And be- 
caufe the artift cannot always communicate his own 
principles, men fpeak of his " happy art," *as if it 
were almoft by chance or hap that his works were 
accomplifhed ; f and it was the fafliion of the laft 
century to fpeak of Shakefpeare himfelf as a wild, 
untutored child of genius, not even to be named as 
an artift, becaufe in truth his plays wanted dramatic 
fcience and were not obedient to the law of the dra- 
matic unities. So that the praife of being a good 
logician, or of having a logical mind, is fometimes 
awarded where there is little or no acquaintance with 
the fcience of logic. An underftanding naturally 
clear, and a certain power of imitation, will enable 
the thinker or fpeaker to pour forth arguments which 
might ferve for examples of all the logical rules, not 
one of which he has learnt ; and without feme lhare 
of thefe talents, no precepts would avail to make a 
reafoner. But when we write upon Logic, the un- 
confcious fkill of the artift muft be left out of the 
account, becaufe it cannot be communicated by rules. 
By the art of Logic we mean fo much of the art of 
thinking as is teachable, and no more. The whole 



* JVherweir* Philofophy of Ind. Sciences, n. p. in. 

f So we have the line of Agatho, Tl^ro tv%w serefe, xetl rv^n 

C 



i8 OUTLINE OF THE 

of every fcience can be made the fubjedt of teach- 
ing.* 

§ 8. In treating of Logic as a fcience, we fhall 
not forget that the ultimate object of the ftudy is 
ftri&ly practical, and fhall labour to ftate the prin- 
ciples in fuch a way as to facilitate to the ftudent 
their application as an art. If we would redeem 
Logic from the charge ufuajly brought againft it, that 
it is a fyftem of rules which the initiated never em- 
ploy, and the uninitiated never mifs, it muft be by 
giving it a far more extenfive verification in practice 
than it ufually receives. The inconfiftency of teach- 
ing a fcience, where we mean that an art fhould be 
ultimately learnt, is only apparent, not real ; and at 
any rate is lefs injurious than that of thofe who teach 
an " inftrumental art *' which is never employed in 
practice, and which is too often inadequate to the 
fimpleft talks of practical application. 

§ 9. Pure Logic is a fcience of the neceffary laws 
of thought. After the remarks already made (in page 
9), this fubjeft will need lefs illustration. Logic only 
gives us thofe principles which conftitute thought ; 
and prefuppofes the operation of thofe principles by 
which we gain the materials for thinking. Thus 
I have a conception of houfe^ which fums up and 
comprifes all buildings in which men live; how 

* AiZaxTTi ivaa-a. iiT^rnfxn fox&jtiai* Arijictle. Eth.Nic. VI. iii. 



LAWS OF THOUGHT. 19 

did I obtain it ? Logic anfwers that it was general- 
ized from different fingle houfes which I had feen> 
by noticing what points they had in common, and 
by gathering up thefe common features into a new 
notion. It teljs us further that this conception has 
various powers, that it may be defined, by declaring 
what I underftand by it, that it may be divided, as 
into " houfes of the rich," and " houfes of the poor," 
that by comparing it with other general notions, as 
church, quay, monumental pillar, I may form a more 
general conception, in which all thefe may be com- 
prehended, that of building. In all this Logic is to 
a certain extent my guide, becaufe conception is one 
great fun&ion of thought; but with confiderable re- 
fervations. It only tells me what is true of all con- 
ceptions, and leaves me to apply the principles to 
this particular one ; for about houfes Logic of courfe 
knows nothing, and to know what is a houfe and 
what not, I muft go to Archite&ure or to common 
experience. Logic only tells me what principles I 
mujl put in pra&ice in forming any general notion 
whatever; but to her all general notions are alike. 
She makes no account of the great diverfity of the 
clafTes of things they reprefent ; king, animal, acid, 
mammal, are all alike to her, and ranked together as 
conceptions, though the fets of objects they feverally 
ftand for, have little refemblance. Logic then takes 
no account of the contents of a conception, of the 



20 OUTLINE OF THE 

things from which it is generalized ; thefe are con- 
tingent to her — if any given clafs from which a con- 
ception is now formed were annihilated, there would 
ftill be conceptions. The fun£tion of conception is 
eflential to thought ; its laws are accordingly laid 
down, but their particular ufe muft be determined by 
the particular fciences. Logic teaches me what Ge- 
neralization, or the forming of common notions from 
many things, is ; but Botany teaches me to general- 
ize upon plants, Political Economy upon the fails of 
focial profperity, Geometry upon the properties of 
fpace, and fo on through the whole range of fciences. 
§ 10. In another direction alfo Logic feems to 
flop fhort, and to leave to another fcience what it 
was incumbent upon it to explain. Our conceptions 
are formed from fingle objefts ; how do we come to 
know thefe ? The logician replies, that it is not his 
bufinefs to fhew how, but that for the mod part they 
are derived from the fenfes, by means of which we are 
put in communication with the external world. But 
many farther queftions arife out of this anfwer. What 
are the fenfes ? How much of every notion conveyed 
by them is new, how much is the refult of the experi- 
ence of paft impreffions ? Does my fight tell me that 
yonder fteeple is about three miles off 5 or is it my 
underftanding co-operating with my fight ? Is there 
no doubt that the fenfes report truly ? Are we even 



LAWS OF THOUGHT. 21 

certain that there is an external world? To thefe 
and many like queftions the logician has one anfwer ; 
— " I prefuppofe a man able to perceive, to receive 
impreffions from the furrounding world, and then 
merely explain the principles on which he muji pro- 
ceed, in combining his impreffions and drawing in- 
ferences from them. The fpeculations you fuggeft 
are highly interefting, and all who would underftand 
the mind of man muft enter upon them ; but the 
fcience of Metaphyfics, or of the Human Mind, has 
already taken them up, and, clofely connected as 
Logic is with this fcience, it is expedient that they 
mould divide the ground. Logic therefore prefup- 
pofes a mind capable of, and actually receiving, im- 
preffions ; though, perhaps, if there were no fuch 
fcience as Metaphyfics, it would be neceflTary even 
in a logical work to give a preliminary account of the 
origin of all knowledge/' 

§ II. Pure Logic is a fcience of the form y or of 
the formal laws of thinkings and not of the matter. 
Though we may doubt the policy of preferving an 
expreffion like form^ the meaning of which, origina- 
ting in a loofe and vague metaphor, is difficult to 
catch and retain, it is fo generally ufed in connexion 
with Logic that fome attempt to explain it feems de- 
manded by our prefent purpofe. 

A ftatue may be confidered as confiding of two 



22 OUTLINE OF THE 

parts, the marble out of which it is hewn, which is 
its matter ox fluff, and the form which the artift com- 
municates. The latter is effential to the ftatue, but 
not the former, fince the work might be the fame, 
though the material were different ; but if the form 
were wanting we could not even call the work a 
ftatue. This notion, of a material fufceptible of a 
certain form, the acceffion of which (hall give it a 
new nature and name, may be analogically transferred 
to other natures. Space may be regarded as matter, 
and geometrical figures as the form imprefTed in it. 
The voice is the matter of fpeech, and articulation 
the form. But as it is the form which proximately 
and obvioufly makes the thing what it is (although 
there can be no form without matter), the word 
form came to be interchanged with ejjence and with 
nature. Already we have left the original fenfe at 
fome diftance. 

§ 12. With thinkers to whom the metaphorical 
fenfe was not fo prominent, the word is ufed in three 
diftin£t but cognate fenfes. It is, iff, a law or an 
idea, which are the fame thing feen from oppofite 
points. " That which, contemplated objeffively (that 
is, as exifting externally to the mind) we call a law ; 
the fame contemplated fubjeffively (that is, as exifting 
in a fubjecft or mind) is an Idea. Hence Plato often 
names Ideas, Laws; and Lord Bacon, the Britifh 



LAWS OF THOUGHT. 23 

Plato, defcribes the laws of the material univerfe as 
ideas in nature. £%uod in naturd naturatd lex^ in na- 
turd naturante idea dicitur" * Lava, heated metal, 
boiling water, the rays of the fun, all rank under one 
common form (that is, law) of heat^ namely : by 
which is meant that they, all and each, contain what- 
ever is efTential to heat. Lead, gold, vermilion, 
ftones, and (in a greater or lefs degree) all bodies, 
pofTefs weight ; the law of weight then is their form 
— the law under which they all come, the condition 
with which they all comply. By virtue of this form 
they are, not bodies indeed, but heavy bodies : in 
Other words, if we fuppofe that form or law to be 
expunged from the tables of the univerfe, their ex- 
iftence as to that nature or property would terminate; 
or if the idea of weight were removed from the mind, 
we could no longer know them as heavy bodies- 

§ 13. Now how does every one of the given in- 
ftances come under the forms, heat and gravitation ? 
By fomething contained within itfelf — by its embo- 
dying the law or definition : that which comes under 
the form of weighty muft: pofTefs weight, muft have 
in it all that the definition of weight demands. And 
here we may trace the fecond meaning of the word 
form : it is that part of any objecl through which it 

* Coleridge's Church and State, p. 12, 



24 OUTLINE OF THE 

ranks under a given law. Every new objeft repre- 
fented to the mind is referred to different laws, called 
forms, by virtue of various qualities in itfelf, each of 
which is termed metonymically, and with refpeft to 
the law under which it is the means of ranking the 
reprefentation, its form. When we obferve (fay) a 
ftone, the mind proceeds to clafs the reprefentation 
of it, afforded by the fenfes, under the various forms 
of colour, figure, fize, weight, temperature, &c. ; and 
with reference to the form (law) of weight, the weight 
of the ftone would be its form (effential part), with 
reference to the form of colour, the greynefs of the 
ftone would be its form. So that that, which in the 
objeft, when viewed in relation to one law or form, 
is its form (effential part), is not its form when it is 
viewed in relation to another. Now the matter of 
any reprefentation is that part of it which with re- 
ference to any given law is non-formal. # Thus in 
our ftone, the weight, fize, temperature are parts of 
the matter, as far as the law of colour is concerned, 
for they are all non-formal, and the colour of the 
ftone alone is formal. The matter is that which, 
when added to the form (efTential part), gives it 



* Hence the fame thing is alternately form and matter. See 
Hitter's Hiftory, hi. p. 121, (Eng. Tranf.) for this point in 
Ariftotle's doclrine. 



LAWS OF THOUGHT. 25 

extraneity — outnefs — objective # exiftence. Without 
fomething more than the mere form, there can be no 
imjiance of a law, an inftance being the prefence of 
the law in an obje£t capable of containing it, and 
thus prefuppofing two things, the law and the capable 
obje£t, whereof we term one the form and the other 
the matter. Ex. gr. triangle may be conceived by 
means of its own form or definition alone, but it 
muft have a material part, it muft become a triangle 
of ftone, or wood, or ink on paper, as the condition 
of its external exiftence. When no feparation, ac- 

* It will be well once for all to explain the modern ufe of 
the words fubjecl and objeB—fubjefllve and objeftwe. The 
fubject is the mind that thinks; the object is that which it 
thinks about. A fubjective impreflion is one which arifes in 
and from the mind itfelf 5 an objective arifes from obfervation 
of external things. A fubjective tendency in a poet or thinker 
would be a preponderating inclination to reprefent the moods 
and ftates of his own mind ; whilft the writer who dwells moft 
upon external objects, and fuffers us to know little more of his 
own mind than that it has the power to reproduce them with 
truth and fpirit, exhibits an objective bias. As the mind how- 
ever fometimes regards its own ftates, of feeling or fenfation, 
as objects, it has been propofed to call them when fo employed 
fubjefl-objefts, i. e. parts of the fubject regarded as objects ; 
whilft purely external things might be called objecls. (Kr tig's 
Phil. Lexicon, under Gegenjland.) Thefe words have under- 
gone great changes of meaning, excellently traced out in Sir 
W. Hamilton's Reid, p. 806, in a note which only the Editor 
of that work could have written. 



26 OUTLINE OF THE 

cording to fome law or other, of a reprefentation into 
its formal and material part takes place, that is, where 
it is referred to no law or conception already in the 
mind, there muft be total ignorance of the object re- 
prefented : the reprefentation muft remain obfcure, 
and can never amount to a cognition. The abfo- 
lutely material part of a cognition would be that 
which remains unknown after it has been brought 
under as many forms as the mind can reduce it to : 
that which never becomes the condition of its rank- 
ing under a law. Forms have a triple mode of exist- 
ence ; they exift in the Divine Mind as ideas, and 
are the archetypes of creation ; they exift as embo- 
died in " inftances " or examples, in which mode 
they are laws ; they exift laftly in the human mind 
as ideas : thus they precede creation, they are in it, 
they fucceed it. 

§ 14. Writers of this fchool give yet a third fenfe to 
the word form ; as it denotes the law, fo by an eafy 
tranfition it ftands for the clafs of cafes brought to- 
gether and united by the law. Thus to fpeak of the 
form of animal might mean, firft, the law or definition 
of animal in general ; fecond, the part of any given 
animal by which it comes under the law, and is what 
it is ; and laft, the clafs of animals brought together 
under the law. 

§ 15. The fenfe attached at the prefent day to the 



LAWS OF THOUGHT. 27 

words form and matter is fomewhat different from, 
though clofely related to thefe. The form is what 
the mind impreffes upon its perceptions of things, 
which are the matter ; form therefore means mode 
of viewing objects that are prefented to the mind. 
When the attention is direited to any objeft, we do 
not fee the obje£t itfelf, but contemplate it in the 
light of our own prior conceptions. A rich man, for 
example, is regarded by the poor and ignorant under 
the form of a very fortunate perfon, able to purchafe 
luxuries which are above their own reach; by the 
religious mind, under the form of a perfon with more 
than ordinary temptations to contend with ; by the 
political economift, under that of an example of the 
unequal diftribution of wealth ; by the tradefman, 
under that of one whofe patronage is valuable. Now 
the obje£t is really the fame to all thefe obfervers ; 
the fame " rich man" has been reprefented under all 
thefe different forms. And the reafon that the ob- 
fervers are able fo to find many in one, is that they 
connect him feverally with their own prior concep- 
tions. The form then in this view is mode of 
knowing ; and the matter is the perception, or objeft 
we have to know.* Hence, when we call Logic a 



* A few pafTages to illuftrate thefe various meanings, may 
be added here. Plato ufes form in all the three fenfes, of law, 



28 OUTLINE OF THE 

fcience of the formal laws, or the form, of thinking, 
we mean that the fcience is only concerned with 
that which is eflential to, and diftin&ive of, the 
thinking procefs. Every a£t of thought, is a thought 
about fomething ; it has matter as well as form. 
Every common noun is a fign of the aft of concep- 
tion ; thus cryftal is a conception formed from com- 
paring together many inorganic bodies which have 
fpontaneoufly affumed certain regular forms ; animal, 
a conception from comparing many live creatures. 
Here the form is the fame, for both are conceptions, 
and it is this quality which conftitutes them thoughts ; 

diftin&ive or eflential part, and fpecies (which laft word means 
form) 5 as thefe places will fhow. 

" Remember then, that I dire&ed you not to teach me fome 
one or two holy a6ls out of many, but that very form by 

which all holy a&s are holy Teach me then, the 

nature of that form itfelf, that looking to it and ufing it for 
our example, I may declare any of the actions of yourfelf or 
any other, which partake of this nature, to be holy, and any 
not fo partaking, not to be holy." — Plat. Euthyp. 6, D. E. 
" And of the juft, the unjuft, the good, the evil, of all the 
forms in fhort, the fame holds true, that each is one and fimple, 
but becaufe every where appearing by incorporation with ac- 
tions, or matter, or other things, that each appears many." — 
Refp. 4.76, a. " For we have been accuftomed to lay down 
one form for many particular cafes, on which we impofe the 
fame name." — Refp. 596, a. " And according to the fame 
form of juftice, a juft man will nowife differ from a juft city, 
but will be like it." — Refp. 4.35, B. See alfo Symp. 205, D. j 



LAWS OF THOUGHT. 29 

but the matter is different, for one is about certain 
inorganic folids, and the other about living creatures. 
Logic, not being concerned with the things that 
thoughts are formed from, ranks the two together : 
it is for Mineralogy and Zoology to diftinguifh be- 
tween them, Logic only knows them for their formal 
or logical value. Are they conceptions ? are they 
judgments, fyllogifms, definitions, or genera? Occu- 
pied only with the bare laws of thinking, Logic muft 
leave to other fciences the confideration of the various 
matters upon which thefe laws operate. In thefe 
thoughts — " life is fhort" — " Mirabeau was faid to 

Refp. 581, E.; Polit. 258, E. Lord Bacon fays, " The form 
of any nature is fuch that where it has place the given nature 
is alio, as an infallible confequence. Therefore it is ever pre- 
fent where the given nature is fo, it attefts that nature's pre- 
fence, and is in it all. The fame form is fuch that upon its 
removal the given nature infallibly vanilhes. Therefore it is 
invariably abfent where that nature is fo, it in thofe cafes difa- 
vows that nature's prefence, and is in it alone." — Nov. Org. 
11. 4. " The examination of forms proceeds thus. Concern- 
ing the given nature we muft firft bring together before the 
intellect all the known inftances, agreeing in that nature, 
though manifefting it in vehicles [i. e. in matter] the moft dif- 
flmilar. ,, — Nov. Org. n. u. Again, " When we fpeak of 
forms, we underftand nothing elfe than thofe laws and mani- 
feftations of the pure a6t, which order and conftitute any fim- 
ple nature, as heat, light, weight, in any fort of matter and 
fubjecl: that can contain them. Therefore, the form of heat 
or form of light, and the law of heat or light is the fame thing, 



30 OUTLINE OF THE 

have been poifoned" — " the radii of a circle are 
equal," we have only one form or law of thinking, 
namely Judgment, exhibited in connexion with va- 
rious things or matter. 

§ 1 6. Logic is faid, in the language of the old 
writers, to be concerned only with fecond notions or 
intentions. The diftin&ion between firft and fecond 
intentions is connected with that which has been 
drawn between matter and form. Notions are of 
two kinds ; they either have regard to things as they 
arej as horfe, Ihip, tree, and are called firft notions ; 
or to things as they are underjiood^ as notions of 

nor do we ever abftraft our thoughts from actualities and active 
manifeftations." — Nov. Org. n. 17. Again, " For fince the 
form of a thing is the very thing itfelf (ipjlffima res), and the 
thing no otherwife differs from the form, than as the apparent 
differs from the exiftent, the outward from the inward, or that 
which is confidered in relation to man from that which is 
confidered in relation to the univerfe [or univerfal mind], it 
follows clearly that no nature can be taken for the true form, 
unlefs it ever decreafes when the nature itfelf decreafes, and in 
like manner is always increafed, when the nature is ina'cafed." 
— Nov. Org. 11. 13. 

Ritter in his Hiftory fhews the analogy between form and 
difference, matter and genus refpeclively, in the writings of 
Arijiotle $ Plotinus indeed afferts their abfolute identity. Ennead. 
11. iv. 4. For a Collection of paffages to illuftrate Arijiotle" s 
doctrine, fee Waifs' Organon. comm. on 94. a. 20. To our 
own great writers the philofophical fenfes of the word form 
were well known. Taylor ', Andrevjes, Hooker , Berkeley, Butler, 



LAWS OF THOUGHT. 31 

genus, fpecies, attribute, fubjeft, and in this refpe£t 
are called fecond notions, which however are bafed 
upon the firft, and cannot be conceived without 
them. The firft intentions precede in order of time, 
for, as Boethius explains, men firft intended to give 
names to things, before they intended to find names 
for their mode of viewing them. Now Logic is not 
fo much employed upon firft notions of things, as 
upon fecond ; that is, as we have faid, it is not occu- 
pied fo much with things as they exift in nature, but 
with the way in which the mind conceives them. A 
logician has nothing to do with afcertaining whether 
a horfe or a fhip, or a tree exifts, but whether one of 
thefe things can be regarded as a genus or fpecies, 



Sir Thomas Brown, Coleridge — fupply inftances which are now 
before us. But the fubjecl: has already occupied our attention 
long enough. KeckermanrC s Logic affords materials for under- 
Handing the views of the old logicians. 

The philofophic value of the terms matter and form is 
greatly reduced by the confufion which feems invariably to 
follow their extenfive ufe. Whilft one writer explains form as 
" the mode of knowing 1 ' an object, another puts it for " dif- 
tinclive part,*' which has to do with the being or nature of the 
thing rather than with our knowledge of it ; where it means 
" fhape" in one place, which is often a mere accident, in ano- 
ther it means " effence j" fo that it may be brought to ftand 
for nearly oppofite things. I will add, that probably there is 
no idea which thefe terms reprefent that cannot be conveniently 
expreffed by others, lefs open to confufion. 



32 OUTLINE OF THE 

whether it can be called a fubje£t or an attribute, 
whether from the conjunction of many fecond no- 
tions a propofition, a definition, or a fyllogifm can be 
formed. The firft intention of every word is its 
real meaning ; the fecond intention, its logical value, 
according to the function of thought to which it 
belongs.* 



* Vox articulata eft fignum conceptus, qui eft in animo : 
duplex autem eft ejufmodi vox, alia namque fignificat concep- 
tual rei, ut homo, animal ; alia vero conceptum conceptus, ut 
genus, fpecies nomen, verbum, enunciatio, ratiocinatio, et aliae 
hujufmodi ; propterea hae vocantur fecundae notiones $ illas 
autem primae. Zabarella de Nat: Log. i. x. 

Prima notio eft conceptus rei quatenus eft, ut animalis, ho- 
minis ; fecunda notio eft conceptus rei quatenus intelligitur, ut 
fubje&um et attributum. Pacius. Anal: Comm. p. 3. a. 

See alfo Buhle {Ariftotle i. p. 432) 5 Crackantkorp, (Logic. 
Procem.) and Sir W. Hamilton in Ed. Rev., No. 115, p. 210. 
There is no authority whatever for Aldricli's view, which 
makes fecond intention mean apparently " a term defined for 
Tcientific ufe $ " though with the tenacious vitality of error it 
ftill lingers in fome quarters, after wounds that mould have 
been mortal. 




OUTLINE OF THE LAWS OF 
THOUGHT. 




LANGUAGE. 

'Ecrr) pay ovv rd hv rrj $ojvyj ruiv lv rfj ^X y ^ 
irocSrji^drwv o^'p^oAa." — Arijl. de Int. 

§ x 7- 
flTHERTO we have affumed that the 

adequate objeft matter of Logic is 
thought^ rather than language ; that 
having explained the laws of thinking, 
it is not bound to examine under what conditions 
thefe manifeft themfelves in fpeech. But logicians 
do not invariably follow this courfe ; thofe who re- 
gard it as an aft of reafoning, feeing that reafoning is 
not conduced but by language, and that many of the 
chief impediments to the correct performance of the 
procefs, lie in the defe&s of expreflion, make fpeech 
and not thought the matter with which they are pri- 

D 



34 OUTLINE OF THE 

marily concerned. The name of Logic itfelf would 
not be inconfiftent with this view \ fince logos may- 
mean the outer or the inner word — the fermo internus 
or the fermo externus — the articulate expreffion or 
the thought itfelf. Here then the relation between 
thought and language muft be afcertained. 

§ 18. Language, in its moft general acceptation, 
might be defcribed as a mode of expreffing our thoughts 
by means of motions of the organs of the body ; it 
would thus include fpoken words, cries and involun- 
tary geftures that indicate the feelings, even painting 
and fculpture, together with thofe contrivances which 
replace fpeech in fituations where it cannot be em- 
ployed, — the telegraph, the trumpet-call, the emblem, 
the hieroglyphic. # For the prefent however we may 
limit it to its moft obvious fignification ; it is a fyftem 
of articulate words adopted by convention to repre- 
fent outwardly the internal procefs of thinking. 

§ 19. But language, befides being an interpreter 



* Language is thus divided by M. Duval- Jouve, Logique, 
p. 201. 

Abfolute— Cries and Geftures. 



Languages 
are 



f Abfolute— Cries and Ge 
Natural I Conventional-^^. " 



Artificial 



Abfolute— Fainting and Sculpture' 
Conventional — Emblems , Tele- 
graphic Signs, Hieroglyphics, 
Writing. 



LAWS OF THOUGHT. 35 

of thought, exercifes a powerful influence on the 
thinking procefs. The logician is bound to notice it 
in four functions — (i.) as it enables him to analyfe 
complex impreflions, (ii.) as it preferves or records 
the refult of the analyfis for future ufe 5 (iii.) as it ab- 
breviates thinking by enabling him to fubftitute a 
fhort word for a highly complex notion, and the like, 
and (iv.) as it is a means of communication. 

§ 20. (i.) The language of words never records 
an impreflion, whether internal or external, without 
fome analyfis of it into its parts. Befides the obje&s 
which we obferve, and their qualities, we can repro- 
duce in fpeech the mutual relations of objects, the 
relations of our thoughts to objects, and laftly the 
order and relation of our thoughts themfelves. Nov/ 
as the mind does not receive impreffions pamvely, 
but reflects upon them, decompofes them into their 
elements, and compares them with notions already 
ftored up, language, the clofe-fitting drefs of our 
thoughts, is always analytical, — it does not body forth 
a mere pi£ture of fa£r.s, but difplays the working of 
the mind upon the fails fubmitted to it, with the 
order in which it regards them. This analyfis has 
place even in the fimpleft defcriptions. " The bird 
is flying" is an account of one obje£t which we be- 
hold, and its prefent condition. But the object was 
Tingle, whilft our defcription calls up two notions — 



36 OUTLINE OF THE 

" bird" and " flying/' — and it is plain that this dif- 
ference is the refult of an analyfis which the mind 
has performed, feparating, in thought, the bird from 
its prefent aftion of flying, and then mentioning them 
together. # In painting and fculpture on the contrary 
we have languages that do not employ analyfis ; and 
a pifture or ftatue would be called by fome afyntbetic^ 
or compofitive, fign, from the notion that in it all 
the elements and qualities of the obje£t which would 
have been mentioned feparately in a defcription, are 
thrown together and reprefented at one view. The 
ftatue of the Dying Gladiator gives at one glance all 
the principal qualities fo finely analyfed by the fol- 
lowing defcription, which however includes alfo the 
poet's reflexions upon and inferences from the qua- 
lities he obferves ; the objective impreffion is defcribed, 
but with a development of the fubjeSfive condition 
into which it throws the narrator, f 

" I fee before me the Gladiator lie : 

He leans upon his hand — his manly brow 

Confents to death but conquers agony, 

And his drooped head finks gradually low — 

And through his fide the laft drops, ebbing flow 

From the red gafh, fall heavy, one by one, 

Like the firft of a thunder-fhower 5 and now 



* See Mr. Smart's Sematology, ch. 1, § 3. 
f P. 25, note. 



LAWS OF THOUGHT. 37 

The arena fwims around him — he is gone, 
Ere ceafed the inhuman fhout which hailed the wretch who 



" He heard it, but he heeded not — his eyes 
Were with his heart, and that was far away 5 
He recked not of the life he loft, nor prize, 
But where his rude hut by the Danube lay, 
There were his young barbarians all at play, 
There was their Dacian mother — he, their fire, 
Butchered to make a Roman holiday ! 
All this rufhed with his blood — fhall he expire 
And unavenged ? Arife ! ye Goths, and glut your ire ! " 

Byron. 

Here the analyfis of the impreffion is carried to its 
farther! ; and in the fecond ftanza the object becomes 
quite fubordinate to the inferences and fancies of the 
fubjedt. But it is all the more ftriking as an illuftra- 
tion of the principle, that language prefents to us the 
analyfis, as painting and fculpture the imitations, of 
a fenfible impreffion. 

§ 21. But different languages are more or lefs 
analytic, and the fame language becomes more ana- 
lytic as literature and refinement increafe.* This 
property indicates, as we mould expe£t, correfpond- 
ing changes in the ftate of thinking in different 
nations or in the fame at different times. With in- 



* See Donald/on, New Cratylus, B. I. ch. 3 ; Dunjal-Jou^ve^ 
Logique, p. 203 5 Damiron, Logique, p. 207. 



38 OUTLINE OF THE 

creafing cultivation, finer diftinftions are ken be- 
tween the relations of obje&s, and correfponding 
expreffions are fought for, to denote them ; becaufe 
ambiguity and confufion would refult from allowing 
the fame word or form of words to continue as the 
expreffion of two different things or fails. Many 
ambiguous phrafes however are fuffered to remain, 
although the inconvenience of them muft have been 
perceived from the firfl: ; thus in Greek, the words 
Yifrova) rskvcov bear the two oppofite fenfes of " plea- 
fures which children feel" and cc pleafures derived 
from one's children," and in Latin metus hojilum 
may mean either c< the fear we have of our enemies," 
or " the fear our enemies have of us." In the Bible, 
words as important as " the love of God" exprefs 
the pious regard we have towards our Father or His 
benignity towards His creatures. Prepofitions are 
our interpreters to clear away this confufion. Again 
where the powers of a particular cafe of a fubftantive 
were once fufficient to denote the perfon whofe 
a£tion the verb defcribed, whilft the pronoun was 
only ufed as an additional mark when great emphafis 
was required, more modern habits, exalting the no- 
tion of perfonahty, always affign a diftinft word to 
the perfon. Thus the Greeks were able to exprefs 
u I have a pain in my head" by three words, 'Axyu 
tav KtcpaMv : they needed no word to diftinguifh the 



LAWS OF THOUGHT. 39 

perfon, and merely qualified the verb by "the head" 
to exprefs the feat of the pain. Our expreffion ana- 
lyfes the verb into three diftinCt notions, " I," the 
perfon, " pain," the thing I fufFer, and " have'' the 
relation ; and fhews more explicitly by the prepofi- 
tion " in" that the head is the feat of the pain. As 
a language acquires more of this character, and mul- 
tiplies pronouns, prepofitions and conjunctions, it 
begins to forget its inflections, becaufe it can exprefs 
all their powers by circumlocution with thefe new 
expletives. As fyntax becomes more complex, in- 
flexions grow Ampler. Our own language has almoft 
loft the terminations of cafes and perfons ; and French 
writers attribute part of the clearnefs of their own 
tongue to the fame caufe, and to the confequent ne- 
ceffity of determining the relations of words clearly 
by proper connectives. The Greek has preferved 
its inflections, although it has alfo acquired a full and 
complicated fyntax ; which is owing probably to the 
fa£t that the Homeric poems moulded and fet the 
former before the neceffity for the latter had arifen. 
Perhaps the Greek of Homer fhews more than its 
original complexity of fyntax, from the touch of later 
editorial hands, like that of Peififtratus. Here then 
is a further ufe of language, and a proof of its inti- 
mate adaptation to thought. As the diftinCtions be- 
tween the relations of objeCts grow more numerous, 



40 OUTLINE OF THE 

involved and fubtle, it becomes more analytic, to be 
able to exprefs them : and, inverfely, thofe who are 
born to be the heirs of a highly analytic language 
muft needs learn to think up to it, to obferve and 
diftinguifh all the relations of obje£ts, for which they 
find the expreffions already formed, fo that we have 
an inftruftor for the thinking powers in that fpeech 
which we are apt to deem no more than their hand- 
maid and minifter. 

§ 22. The fuperiority of fpoken language over the 
language of painting and fculpture, has been the fre- 
quent fubjeft of remark. One reafon for it is that 
whilft the artift can only effe£t with certainty an im- 
preffion upon the eye, and muft depend upon the 
fenfibility, often imperfeft, of the fpe&ators for the 
reproduction in their minds of the emotions that fug- 
gefted his fubje£t and guided his hand, the poet by 
his defcription can himfelf call up the appropriate 
feelings. Upon the forehead of the Dying Gladiator 
what chifel could infcribe plainly that which the poet 
bids us read there ? 

— " his manly brow 
Confents to death but conquers agony. " 

In the picture of the Crucifixion at Antwerp, by 
Rubens, one of the moft powerful fpecimens of u the 
brute-force of his genius," the action and purpofe of 
more than one of the figures have been variously 



LAWS OF THOUGHT. 41 

underftood, and therefore by one party or another 
mifunderftood. It is a difputed queftion whether the 
mounted foldier is looking with reverence at the chief 
Figure, or with cruel calmnefs at the agonies of one 
of the thieves ; and whether the foldier on the ladder 
has broken the legs of the thief, or is preparing to do 
fo. Art finds few to underftand its fweet inarticulate 
language ; but the plainer and fuller utterances of 
poetry cannot be mifunderftood. Another reafon of 
its fuperiority may be found in the greater power of 
words to fuggeji ajfociations that knit up our prefent 
impreffion with others gained from the paft, or, bet- 
ter ftill, bring our emotions and moral feelings into 
connexion with our prefent impreffion. What paint- 
ing of a houfe can ever convey fo much to a feeling 
heart as the fhort defcription — " This is the home 
in which I fpent my childhood ? " The fculptor 
raifes a tomb, and covers it with the enfigns of piety 
and death, but his art tells us lefs after all than the 
brief infcription, " He died for his country," or, " he 
looks for immortality." # The painter cannot dip 
his pencil in the hues of the fpirit ; the fculptor's drill 
and chifel cannot fix in matter the fhapes which the 
mind affumes. The artift's thought remains unex- 



* Compare Coujin, Philofophie du Vrai, &c. legon 27 j and 
Burke , on the Sublime, § vii. 5. 



42 OUTLINE OF THE 

plained, or depends upon the cafual advent of conge- 
nial interpreters. In the comments upon our famous 
pictures and ftatues we have fo many acknowledg- 
ments of the inferiority of the language of art to that 
of fpeech. Art would need no commentators, if it 
were thoroughly competent to tell its own ftory. 

§ 23. (ii.) Thefecond function we afcribed to lan- 
guage was that of preferving and recording our 
thoughts for future ufe ; nomina funt notionum notes. 
A difcovery can hardly be faid to be fecured, until it 
has been marked by a name which fhall ferve to re- 
call it to thofe who have once mattered its nature, and 
to challenge the attention of thofe to whom it is flill 
flrange. Such words as inertia, affinity, polariza- 
tion, gravitation are fummaries of fo many laws of 
nature, and are fo far happily chofen for their pur- 
pofe, that, except perhaps the third, each of them 
guides us by its etymology towards the nature of the 
law it ftands to indicate. When Gay LufTac and 
Mitfcherlich difcovered that fome chemical fubftances 
either cryftallize in the fame form, or may be fubfti- 
tuted for one another in compounds without change 
in the form which the compounds aflume, they were 
not content with a ftatement of this beautiful and 
inftrudtive law, but they invented the name of ifo- 
morphifm (tendency to equal forms) to be an index 
and fummary of the law and the experiments that 



LAWS OF THOUGHT. 43 

illuftrated it. When two oppofite theories of medi- 
cine are termed Homoeopathy and Allopathy, thefe 
two compound words contain in fact an account of 
the oppofing theories. A recent popular and in- 
structive book* has reminded us that it is poffible to 
exhume from under the words that are their monu- 
ments, many a buried and forgotten theory. Thus 
we fpeak of a jovial, a faturnine or a mercurial tem- 
per, without remembering that this implies an as- 
cription of its qualities to the planet Jove or Saturn 
or Mercury. Phyfiologifts now ignore the fyftems 
from which fuch terms as animal fpirits, good humour, 
vapours, proceed. But if words often ferve as tomb- 
ftones, and remain when the theory has mouldered 
away, they are as often the keys by which we unlock 
the cafket of the living and precious difcovery, to ex- 
hibit it to the world. On the other hand, our emi- 
nent anatomift, Profeflbr Owen, complains of the 
embarraflments produced in his fcience, by having to 
ufe a defcription where a name would ferve ; for in- 
ftance, a particular bone is called by Soemmering 
" pars occipitalis ftric~te fie dicta partis occipitalis 
oflis fpheno-occipitalis," + a defcription fo clumfy that 

* Trench on the Study of Words. Parker, 1851. A lo- 
gical ftudent will find both amufement and profit in the little 
volume. 

f See Owen on the vertebrate ikeleton in Report of Britifk 
AfTociation for 184.6. 



44 OUTLINE OF THE 

we may be certain the bone will not be mentioned 
more frequently than abfolute need requires. In 
many cafes, the privilege of giving the name which 
all the world fhall employ, is conceded to the man 
or the nation who firft clearly perceives the attributes, 
fees that they make one notion, and determines how 
it fhall be defignated. We are indebted to the finer 
obfervation of the French for the names ennui, nai- 
vete, and fineffe, for which we have given our own 
comfortable # in exchange : and an Englifhman may 
notice with a fmile of fatisfadtion that das gentleman- 
like makes its appearance in a German author. 

§ 24. But it is not only in the higher laws of 
fcience, or the more fubtle qualities which focial re- 
finement developes in men and in fociety, that the 
power of naming is the power of fixing the fleeting 
colours of thought. So long as we are content with 
the bare reception of vifual impreffions, we can in a 
meafure difpenfe with words, becaufe our remem- 
brance of the image of each object will ferve inftead 
of its name to ourfelves, and a pi£lure of it may re- 
prefent it, though by a cumbrous and difficult procefs, 
to the minds of others. But thought never flops 
with the mere infpe&ion of obje<fts. In the fimpleft 

* " Mot Anglais," fays M. F hilar ete-Chajles (ix. p. 16), 
" ne (Tun vieux mot Fra^ais." But confortare is found in 
the Latin of the Vulgate."" 



LAWS OF THOUGHT. 45 

cafe, we proceed to decompofe the fenfitive impreffion 
into its parts. The tree which our eyes behold is 
found upon reflection to be tall or ftunted, blooming 
or withered, old or young, ftraight or gnarled, waving 
in the wind or ftill ; and thefe properties have no in- 
dependent exiftence, but are parts of the vifible ob- 
ject; they are entia rationis^ and exift feparately in the 
mind alone. Whence then is our power of recalling 
them with fuch marvellous precifion and facility ? 
How is it that we can keep them fafely apart in the 
mind, inftead of being obliged to look for them min- 
gled and confufed, in the objects from which we firft 
difentangled them by reflection ? By virtue of the 
name we have attached to each of them ; which, 
like the labels upon the chemift's jars or the garden- 
er's flowerpots, enable us at once to identify and fe- 
cure the property we feek. Names then are the 
means of fixing and recording the refult of trains of 
thought, which without them muft be repeated fre- 
quently, with all the pain of the firft effort.* 

§ 25. (iii.) Leibniz was the firft, fo far as I know, 
to call attention to the fact that words are fometimes 
more than figns of thought ; that they may become 
thoughts. His diftinftion between fymbolical and in- 

* Upon this, confult Damiron, Logique, p. 200, feq. and 
Duval- J owve, Logique, p. 199, feq.; Mill, on the Human 
Mind, vol. i. p. 86. 



46 OUTLINE OF THE 

tuitive [notative'] conceptions * conducts us to the 
third function of language, that it abbreviates the 
procefTes of thought. Where our notion of any ob- 
ject or objects confifts of a clear infight into all its 
attributes, or at leaft the effential ones, he would call 
it intuitive. But where the notion is complex, and 
its properties numerous, we do not commonly realize 
all that it conveys ; the procefs of thinking would be 
needleflly retarded by fuch a review. We make ufe 
of the name commonly given to the notion as a fym- 
bol, even for ourfelves, of all the properties it pof- 
feffes. A name then, employed in thought, is called 
a fymbolica I cognition ;, and the names we employ in 
fpeech are not always fymbols to another of what is 
explicitly underftood by us, but quite as often are 
fymbols both to fpeaker and hearer, the full and exact 
meaning of which neither of them flop to unfold, 
any more than they regularly refledt that every fove- 
reign which pafles through their hands is equivalent 
to 240 pence. Such words as the ftate, happinefs, 
liberty, creation, are too pregnant with meaning for 
us to fuppofe that we realize their full fenfe every 
time we read or pronounce them. If we attend to 
the working of our minds we fhall find that each 
word may be ufed, and in its proper place and knk^ 

* Erdmanris Ed. p. 79. A£ta Erudit. an. 1684, 



LAWS OF THOUGHT. 



47 



though perhaps few or none of its attributes are pre- 
fent to us at the moment. A very fimple notion is 
always intuitive \ we cannot make our notion of 
brown or red fimpler than it is, by any fymbol. On 
the other hand a highly complex notion, like thofe 
named above, is feldom fully realized — feldom other 
than fymbolical. Here then is a farther ufe of names ; 
they ferve to abbreviate the procefs of thought, as 
we have feen that they are ufeful in recording its re- 
fults. And it may be noticed here that this diftinc- 
tion of cognitions throws a new light on the nature 
of definitions, or explanatory propofitions, which are 
not, as they are often regarded, mere explanations to 
others of a meaning which we ourfelves duly appre- 
hend, but are real a&s of thought, which by unfold- 
ing before us fome marks of our conception, partially 
or wholly unfeen by us, have all the power of new 
truths even for ourfelves. 

§ 26. (iv.) That language has a fourth ufe, the moft 
obvious of all, as the medium of communication be- 
tween mind and mind, needs no explanation. We 
might difpenfe with articulate fpeech for certain pur- 
pofes, and might make geftures and changes of the 
countenance, which are the language of action, fup- 
ply its place. But a£tions and the play of features, 
whilft they ferve to exprefs love or hatred for fome 
prefent object, need of food or reft, joy or forrow, 



48 OUTLINE OF THE 

can but exprefs a very fmall and confined lift of 
thoughts. If we would indicate our feelings towards 
fome abfent perfon, or our wifh for fomething at a 
diftance, or direct attention to fome inward ftate or 
fentiment, we cannot guide the thoughts of the fpec- 
tator to the object prefent to our own mind, with 
any precifion and certainty. Hence it is necefTary 
to appropriate to every object a fignal, always availa- 
ble, which all men by a tacit convention accept as a 
fubftitute for the object, and which therefore recalls 
the object to the fancy whenever it is employed ; 
and fuch a fignal is a noun or name, defined by 
Ariftotle to be " a found which by convention is 
fignificant, but does not determine time." # The 
convention or agreement by which a whole nation 
confines a noun to one object or clafs of objects, is 
of courfe merely tacit ; whatever theory of the origin 
of language we adopt, we cannot fuppofe that a na- 
tion ever formerly met and agreed upon the feveral 

* "ovofAct, fx&v ovv \gh>\ <f>cov^ cnfAavrmrt Kara a-vvQwnv anv %p6vov, hg 
fxnlh (A2po$ Wt\ crvpavTiHov xsxapia-fAwov. On Enounc 'e 'ment , ch, 2. 
(The laft words exprefs that it divides into fyllables only, and 
not words, otherwife it would be a fentence.) e Tri(xa (verb) £e 
la-rt to 7rpocr(rri(xa7vQv x?° vov * c ^* 3* J* £• Scaliger traced the 
diftin&ion between the noun and the verb to a difference of 
time, for the noun reprefented a permanent thing, the verb a 
temporary and tranfitory ftate. 



LAWS OF THOUGHT. 49 

names that fhould thenceforward exprefs their va- 
rious notions. Language is bafed upon general 
agreement, if we give our aflent to its ufe every day 
by hearing and anfwering it, juft as truly as if the 
view of Maupertuis were correct, that language was 
originally formed by a feffion of learned focieties. 
Names however are reprefentatives of things \ and 
the different ftates of things muft find an expreffion 
likewife ; hence the need of adjeftives and verbs. 
The verb has the power of affigning to the thing at 
a particular time the condition of being, doing, or 
undergoing fomething; but as every verb may be 
refolved into an adjeftive-notion, and one particular 
word fimply expreffive of paft or prefent or future 
ftate, as for example, " he loved" is explained by 
" he was— loving," " he hopes" by a he is — hoping," 
we are juftified in regarding all verbs as fundamen- 
tally one, the verb to be, with its three times or tenfes 
of is j was, Jhall be, and their variety as arifing from 
the incorporation of various adjeftive-notions with 
this fimple verbal element. When two or more 
names come together, it is frequently neceffary to 
exprefs the mutual relation in which they ftand ; a 
thing may be to, from, by, in, near, above or below 
another, and prepofitions are invented to determine 
this. Here then are the four principal parts of fpeech, 
fubftantives, or names to exprefs fubftances, adjeftives 

E 



50 OUTLINE OF THE 

to ftand for attributes, prepofitions to denote rela- 
tions, and a fingle verb to affign attributes or rela- 
tions to fubftantives at a determinate time. # 

§ 26. Ariftotle's mode of arranging the claffes of 
words admits of a brief, and (it may be hoped) intel- 
ligible ftatement. Words are conventional figns of 
what takes place in the mind; natural figns, as a 
fcream to exprefs terror, a fcowl for hatred, a laugh 
for pleafant furprife, are not to be ranked among 
them. The queftion whether fome founds are not 
naturally more fuitable to certain ideas, for examples, 
the found ofy? to exprefs ftrength and folidity, in 
ftand, ftout, fturdy, ftick, flop, ftubborn, or the 
found of wr to exprefs turning with an effort, as in 
wring, writhe, wreft, wreftle, wrift, is pafled over ; 
and it is evident that even if the founds are fuitable 
to the ideas they exprefs, there was no neceffity for 
adopting them, and they are, like the reft, fubjedr. to 
a tacit convention. Now fome words, or rather 
vocal founds, are fimple, and confift of parts which, 
taken feparately, have no meaning, or at leaft are not 



* See Condillac Grammaire, ch. viii. The more advanced 
fcudent will not fail to notice that as the ten Categories of 
Ariftotle anfwer to the parts of fpeech, fo the fimpler divifion 
of categories adopted by many later writers, into fubitance, 
attribute and relation, anfwers to three parts of fpeech. See 
below, the Section on Categories. 



LAWS OF THOUGHT. 51 

intended to have any in their prefent pofition ; fuch 
are the fingle founds which we call words, as weapon, 
free, hardfhip, mafter, in which the components -fhip 
and maft- have loft their proper meaning on entering 
into their feveral words. Some again are more com- 
plex, and are not only fignificant themfelves, but 
confift of fignificant parts -, thefe are what we call 
propofitions or fentences, as The fun has fet. Fol- 
lowing firft the fimple words, we find that feme of 
them exprefs a ftate or action at a given time, and 
are known as verbs ; others again are irrefpective of 
time, and are called nouns. Of nouns, feme have a 
knCe independent of any auxiliary words, and there- 
fore can be employed alone as terms in a propofition, 
as city, wildernefs, revenue^ others require the aid 
of other words to complete and determine their 
meaning, as — of a city, good, to Greece, which 
prompt the queftions, what part of a city ? Good 
what ? What happened to Greece ? and therefore 
are not complete in themfelves. The former, pro- 
perly fpeaking, are perfect nouns or names, but the 
latter, which include all cafes of nouns except the 
nominative, are only parts of compound names, and 
require an addition to complete them. If a verb is 
added to one of the imperfect names, there will not 
be an intelligible fentence. Perfect names again 
might be either definite or indefinite, though the 



52 OUTLINE OF THE 

latter, which are nothing more than nouns with a 
negative prefix, as non-philofopher, are hardly worthy 
to be called names, both becaufe they reprefent too 
large a number of objects, and becaufe we explain 
them by faying what they do not mean. Turning 
now from fimple words to propofitions, we notice 
that fome fentences are declaratory, as All muft die ; 
others are only precatory or exclamatory, as a Oh 
that this too too folid flefh would melt ! " Truth and 
falfehood, with the inveftigation of which Logic is 
concerned, belong only to the declaratory propofi- 
tions, and indeed thefe only can truly be called pre- 
pofitions. 

DIVISION OF WORDS. 

(See Ariftotle on En. Ch. i — iii.) 

Whofe parts have C Verbs f Definite 

no meaning — \ f Perfect J 

fimple words. ^ Nouns < I Indefinite 

I Imperfecl 



Words *{ 



Whofe parts have 
meaning — fen- 
tences. 



Declaratory — true or 
falfe propofitions. 

Not declaratory, as a 
prayer or wifh. 



§ 27. It is the province of Univerfal Grammar to 
examine the means of oral and written communica- 
tion, and their laws ; and the hints here offered are 
rather intended to fuggeft than to fuperfede a further 



LAWS OF THOUGHT. 53 

ftudy of that fcience ; to which alone belong the de- 
tails of the do&rine of the Parts of Speech and their 
conftrudtion. Our bufinefs has been to point out 
the principal ufes of language in aiding the procefs of 
thought. But great as thefe fervices are, it muft not 
be fuppofed that an examination of the rules of lan- 
guage would anfwer every purpofe of a logical fyftem. 
As we are now conftituted, our thoughts are inva- 
riably clothed in fpeech •> we ufe words even if we 
do not utter them. But if articulate fpeech were 
withdrawn from man, it cannot be fuppofed that 
thought would for ever ceafe. On the contrary, 
wherever perfonal defeats or external circumftances 
deprive the mind of this means of communication, 
it fucceeds in providing an efficient fubftitute, and 
attains by practice much the fame facility in the ufe 
of it as we enjoy in the exercife of the powers of 
fpeaking. Thofe among the deaf-and-dumb who 
have been taught by the pains of an enlightened hu- 
manity to converfe and to think, muft ufe, inftead of 
the remembered words which we employ, the re- 
membered images of hands, in the various combi- 
nations of finger-fpeech, as the fymbols of their 
thoughts. The deaf-and-blind, taught the names of 
objects from raifed letters, muft think, not by aiTo- 
ciations of found but of touch. The telegraph, and 
the fignals on railroads, are new modes of fpeech ; 



54 OUTLINE OF THE 

and though an inexpert practitioner may have at firft 
to tranflate fuch figns into common language, the 
(kill which comes from pradtice foon prompts him 
to omit this needlefs intermediate ftep. The engine 
driver fhuts off the fteam at the warning fign, without 
thinking of the words to which it is equivalent ; a 
particular fignal becomes aflbciated with a particular 
aft, and the interpofition of words becomes fuper- 
fluous. Dr. Hooke, the inventor of the telegraph, 
called it " a method of difcourfing at a diftance, not 
by found but by fight ;" and it is conceivable that 
we might learn to think by the telegraphic fignals, fo 
that " red flag over blue," ken with the eye or re- 
called by the memory, might be our word for happi- 
nefs. Leibniz (Nouv. EfT. iii. i) fuggefts the poffi- 
bility of employing various tones inftead of articulate 
words to convey our notions ; and mentions that the 
Chinefe, having a flender vocabulary, ufe the aid of 
tone and accent to vary and augment it. The Ranz- 
de$-vaches that rends afunder the heart of the Swifs 
exile, to him is but a word for " country and home;" 
and the fignet of the king fent to his fervant, or the 
broken aftragalus, by which the " gueft-friend " re- 
minded his fellow of his plighted hofpitality, are figns 
which plainly and certainly fuggeft thoughts, and 
therefore they are words alfo. Without thought, 
language would ceafe ; but we can conceive the Ian- 



LAWS OF THOUGHT. 55 

guage we ufe might be denied to us, and yet thought 
ftill proceed with the afliftance of fome other clafs of 
figns. And it is fcarcely philofophical to found an 
analyfis of the reafoning powers upon that which, 
however ufeful to the reafon, may be conceived to 
be univerfally, as it is now in ifolated cafes, feparated 
from it, without deftroying its a£tion. Granting that 
the procefles of thought may be traced to a great ex- 
tent in the figns which it employs, they are ftill but 
figns, and if the procefs beneath them can be exa- 
mined in itfelf — as we need not fear to maintain that 
it can — then to view it only in the inftruments it 
ufes is to leave our furvey mallow and incomplete* 
Logic mould expound the laws of thinking, and uni- 
verfal Grammar the laws of fpeech, apart from their 
fpecial modifications in any given language. Thefe 
two fciences would mutually illuftrate each other ; 
whilft a clear feparation between them would proba- 
bly have the effect of elevating the latter into an im- 
portance not hitherto afligned it. But no confufion 
can refult from introducing principles of language 
into Logic, as has been often done, fo long as think- 
ing is made the adequate object matter of the fci- 
ence, and language comes in only as the minifter of 
thought. 

§ 28. The queftion we have juft confidered — 
whether thinking could proceed without articulate 



56 OUTLINE OF THE 

words as its figns — muft be diftinguifhed from the 
more difficult one — whether thinking could difpenfe 
with all figns. The latter we do not pretend to an- 
fwer here ; but it may be hinted that thinking and 
fcience are not identical, that even if trains of fyfte- 
matic reafoning are quite beyond the reach of any 
but a fpeaking, "word-dividing" being, the fimpler 
a6ts of thought may perhaps be within his reach. 
Without language, all the mighty triumphs of man 
over nature which fcience has achieved would have 
been impoflible. But this does not prove that man 
might not, without fpeech, obferve obje&s, gather 
them into groups in his mind, judge of their proper- 
ties, and even deduce fomething from his judgment. 
Weak and incomplete the procefs of thought would 
be y but we dare hardly fay that one could not think 
at all. But in no fubjeft is it more neceffary to dif- 
tinguifh between the a<5tual, and the merely conceiv- 
able. Language and thought have never been put 
afunder, but in a few exceptional cafes. With fome 
nations they have the fame name \ with all, the rules 
of the one are readily applied to the other. 

§ 29. The opinions about the origin of language 
may be divided into three clafles, as follows. 

a. The belief that man at his creation was en- 
dowed with a full, perfect and copious language, and 
that as his faculties were called forth by obfervation 



LAWS OF THOUGHT. 57 

and experience, this language fupplied him at every 
ftep with names for the various objects he encoun- 
tered. In this view, which has found many able 
advocates, fpeech is feparated from, and precedes, 
thought; for as there muft have been a variety of 
phaenomena both outward and in his mind, to which 
the firft man was a ftranger, until long experience 
gradually unfolded them, their names muft have been 
entrufted to him long before the thoughts or images 
which they were deftined ultimately to reprefent, 
were excited in his mind. 

b. The belief that the different families of men, 
impelled by neceffity, invented and fettled by agree- 
ment the names that ftiould reprefent the ideas they 
poflefTed. In this view language is a human inven- 
tion, grounded on convenience. But u to fay that 
man has invented language, would be no better than 
to affert that he has invented law. To make laws, 
there muft be a law obliging all to keep them ; to 
form a compadt to obferve certain inftitutes, there 
muft be already a government protecting this com- 
pact. To invent language, prefuppofes language al- 
ready, for how could men agree to name different 
objects, without communicating by words their de- 
figns ? " In proof of this opinion, appeal is made to 
the great diverfity of languages. Here it is fuppofed 
again that thought and language were feparate, and 



53 OUTLINE OF THE 

that the former had made fome progrefs before the 
latter was annexed to it. 

c. The third view is, that as the Divine Being 
did not give man at his creation a£hial knowledge, 
but the power to learn and to know, fo He did not 
confer a language but the power to name and de- 
fcribe. The gift of reafon, once conveyed to man, 
was the common root from which both thought and 
fpeech proceeded, like the pith and the rind of the 
tree, to be developed in infeparable union. With 
the fir ft infpe&ion of each natural objeft, the fir ft 
impofition of a name took place ; " Out of the ground 
the Lord God formed every beaft of the field, and 
every fowl of the air ; and brought them unto Adam 
to fee what he would call them ; and whatfoever 
Adam called every living creature, that was the name 
thereof." (Gen. ii. 19.) In the fulleft fenfe, lan- 
guage is a divine gift, but the power and not the re- 
fults of its exercife, the germ and not the tree, was 
imparted. A man can teach names to another man, 
but nothing lefs than divine power can plant in an- 
other's mind the far higher gift, the faculty of naming. 
From the firft we have reafon to believe that the 
functions of thought and language went together. A 
conception received a name ; a name recalled a con- 
ception ; and every acceffion to the knowledge of 
things expanded the treafures of expreffion. And 



LAWS OF THOUGHT. 59 

we are entangled in abfurdities by any theory which 
aflumes that either element exifted in a feparate ftate, 
antecedently to the other. 

§ 30. It is impoffible to trace the growth of lan- 
guage with certainty ; but it is moft probable that 
many of the roots of the primitive language were ori- 
ginally imitations of the various founds emitted by 
things in the natural world. A bird or animal per- 
haps received a name derived from, and refembling, 
its own peculiar utterance. The cry or exclamation 
that man emitted inftinctively under the prefiure of 
fome ftrong feeling, would be confcioufly reproduced 
to reprefent or recal the feeling on another occafion ; 
and it then became a word, or vicarious fign. Where 
natural founds failed, analogy would take the place 
of imitation ; words harm and difficult to pronounce 
would be preferred to ftand for unpleafing objects, 
over thofe of a more bland and facile character, 
which would be appropriated to pleafant things and 
conceptions. Mere agreement among thofe who ufed 
the language, would be fufficient to ftamp a vocal 
found as the name of a certain object, where neither 
imitation nor analogy fuggefted one. But thefe ori- 
ginal roots, the fimpleft form of fubftantives, would 
gradually become lefs and lefs difcernible as the lan- 
guage grew richer and more intricate. Wherever 
new arts are practifed, we may eafily find opportuni- 



60 OUTLINE OF THE 

ties of watching the growth of new names for its 
inftruments and procefles, guided by thefe three prin- 
ciples, imitation, analogy and mere convention. 

§ 31. The various parts of fpeech took their ori- 
gin from the noun and verb, or poffibly from the 
noun alone.* Many inftances can be found of ad- 
verbs and prepofitions which are diftin&ly fubftan- 
tives, and of conjunctions which are but parts of 
verbs. Then the clofe connexion between the verb 
and noun is indicated by the number of words which, 
in our own language, are both verb and noun, and 
only diftinguifhed by mode of pronunciation. In- 
flexions perhaps originated in the addition of one 
word to another, fo that the terminations of nouns 
and verbs are in reality diftinft words incorporated 
with them. Thefe are but flender hints of the direc- 
tion in which profound and acute refearches have 
been made. And I do not think that fuch attempts to 
difTeft and analyfe the language, purfued with proper 
caution, tend at all to lower our eftimate of the impor- 
tance of the gift of fpeech, or of its marvellous nature. 
It is not more wonderful furely that the Giver of Good 
has endowed man with a complete language, than that 
He has endowed him with faculties which out of the 

* " Omnes Hebreae voces, exceptis tantum interjeclionibus 
et conjun&ionibus, et una aut altera particula, vim et proprie- 
tates nominis habent." Spinoza, Gram. Heb, 5. 



LAWS OF THOUGHT. 61 

fhrieks of birds in the foreft, the roar of beafts, the 
murmur of rufhing waters, the fighing of the wind, 
and his own impulfive ejaculations, have conftructed 
the great inftrument that Demofthenes and Shak- 
fpeare and Maffillon wielded, the inftrument by which 
the laws of the univerfe are unfolded and the fubtle 
workings of the human heart brought to light. But 
in no line of enquiry is caution more necefTary, are 
deductions more likely to be fallacious. It does not 
follow that a word as we ufe it now bears a grofs, 
narrow or material fenfe, becaufe the root to which 
we can refer it had a limited meaning, and was con- 
nected with matter. If truth according to its ety- 
mology means that which we trow or think, accord- 
ing to long ufage it means that which is certain 
whether we think it or not ; if fpirit meant originally 
no more than breath, it has fo far left that fenfe be- 
hind, that when the breath is exhaled the fpirit re- 
mains immortal.* 

* On the origin and growth of Language fee Herder Ur- 
fprung des Spr aches (a prize EfTay). Ranch's Psychology , New 
York, 1840. Tooke^s Di<verJions of Purley. Harrises Hermes. 
Donaldfon's New Cratylus. ManfeVs Prolegomena, p. 17, Cou- 
Jin, Frag. Philof. on Maine de Biran. Dwval-Jou^ve Logique, 
§^189, feq. P tarts Cratylus. 



OUTLINE OF THE LAWS OF 
THOUGHT. 

c Hujus difciplinae fhidium atque cognitio in principiis quidem 
tetra et afpernabilis infuavifque efTe et inutilis videri folet : 
fed ubi aliquantum procefferis, turn denique et emolumen- 
tum ejus in animo tuo dilucebit, et fequetur quaedam difcen- 
di voluptas infatiabilis." Aulus Gellius. 

INTRODUCTION concluded. 

§33- 
OGIC has been called an a priori fcience. 

The diftin£lion between truths a priori 

and truths a po/leriGri^ as obferved uni- 

verfally by modern writers, may be 

drawn as follows. If there are any truths which the 

mind poflefles, whether confcioufly or unconfciouily, 

before and independent of experience, they may be 

called a priori truths, as belonging to it prior to all 

that it acquires from the world around. On the 

other hand, truths which are acquired by obfervation 

and experience, are called a pojieriori truths, becaufe 




LAWS OF THOUGHT. 63 

they come to the mind after it has become acquaint- 
ed with external facts. How far a priori truths or 
ideas are poflible, is the great campus philofophorum^ 
the great controverted queftion of mental philofophy. 
In entering into it, and that only fo far as our pre- 
fent purpofe requires, we muft remove from it one 
great caufe of mifunderftanding. No one at prefent 
maintains that the mind can know anything at a 
point of time before its obfervation of external things 
began ; a mind in that condition would be full of 
thick darknefs. However independent of experience 
any procefs may appear to be now, as for inftance, 
that by which geometrical truths are proved, we may 
be fure that we made much ufe of obfervation before 
we educed the very laws which place it in our minds 
far above all need of confirmatory evidence from ob- 
fervation. A mind which never obferved, would not 
be a mind. But the queftion is whether even the 
fa£ts which we obferve do not furnifh evidence that 
fomething has been in the mind before it was direct- 
ed to the fa£ts ; juft as we know by looking at fome- 
thing that we have eyes, and muft have had them 
before we looked, although without putting them to 
their proper ufe we could never have known that we 
had them at all.* Nov/ without going into the dis- 
pute as to how much of our knowledge is a priori^ 

* Coleridge. Lit. Rem. i. 326 $ and Friend, i. 307, note. 



64 OUTLINE OF THE 

we may be able to fhow that at leaft the conditions 
of all knowledge are fo, — that the mind does not 
fimply reflect the images of things without, but im- 
preffes characters of her own upon them, — that our 
knowledge of things is not the exaft counterpart of 
the things, but of the things and the mind operating 
together. When we fee our image in a mirror, (to 
ufe Bacon's fimilitude) we know that our fhape is 
the caufe of it on the one fide and the power of re- 
flexion in the mirror on the other ; if we were to 
fee it multiplied, or increafed, or diminifhed, or 
changed in hue, we ftiould infer that the mirror had 
feveral angular faces, or was concave, or convex, or 
made of tinted glafs. Each of thefe properties would 
be inherent in the mirror prior to our prefenting our- 
felves before it ; they are its a priori laws ; although 
we could only afcertain them a pofteriori, by a trial. 
When an image is received upon the mirror of the 
mind, we fee that the latter alfo has its laws and 
properties. Our remark upon one objeft of common 
occurrence is " the bird is flying againfl: the wind." 
Have we here no more than the fingle objeft which 
the eye prefents ? There are three diftinft notions, 
of a bird, of its being in the aft of flying, of the di- 
rection of its flight ; fo that the mind has decompofed 
the one objeft into three impreflions; and there is 
befides an aft of deciding upon the agreement of 



LAWS OF THOUGHT. 65 

thefe impreffions, exprefled by the word " is." And 
as the obje£t does not refolve iff elf into three parts, 
but is to all intents and purpofes one, and as there 
can be nothing in the objedt to correfpond to the 
a£t of judging exprefled by the word " is," we con- 
clude that the power of analyfis of the fimple im- 
preffion into three, together with that of judging 
upon it, belong to the mind itfelf. Further, as we 
have no reafon to think that this obje£t created the 
two powers, or did more than call them into adtion, 
we conclude that they were prefent a priori^ that is, 
prior to the impreffion from without. And again, 
for the fame reafon that they are not found in this 
obje<5t of fenfe, — that is, becaufe they decompofe it 
into many parts and judge upon its parts, which no 
objeft can do for itfelf — we conclude that they were 
not learnt from any objedt we may have {ten before ; 
and therefore they are abfolutely a priori^ they are 
independent of all experience.* 

* The various modes of exprefling the antithefis between 
thoughts and things are here exhibited in a tabular form. 
Man, . as oppofed to Nature 



Thoughts, 


9> » 


Things 


Theories, 


99 99 


Fa&s 


Reflection, 


>> ?> 


Senfation 


Subject, 


>> » 


Object 


Form, 


3> >J 


Matter. 


IVheiveWi 


* Phil. 


of Ind. Sci. 



66 OUTLINE OF THE 

§ 34. Hence we may underftand the importance 
which attaches to Leibniz's well known comment on 
the maxim of the fchool of Locke ;* to the nihil eft 
in intelleffu, quod non fuerit in fenfu^ he adds — niji 
intelleflus ipfe. The mind does not fimply receive 
the impreffions of the fenfes, like the paffive furface 
of a mirror; it groups them, judges about them, fe- 
parates their qualities from each other, and draws 
inferences about the qualities which like objefts, 
hitherto unknown, may be expected to have. But 
qualities, clafTes, inferences, are not objedts of knkj 
however they may refide in or be drawn from thofe 
objects. They have no feparate exiftence out of the 
mind ; whilft, within it, they are perfectly diftinft. 
This tranfmutation of objects of fenfe into their ele- 
ments muft therefore be the work of the mind alone. 
It is a law of the intellect itfelf, and never was nor 
can have been in the fenfuous impreffions we have 
received. 

§ 35. Pure Logic treats only of thofe laws or con- 
ditions to which objects of fenfe are fubje£ted in the 
mind : and hence it is called an a priori fcience. It 
unfolds the laws of the intelleSfus ipfe^ and gives no 

* Leibniz. Nowveaux EJfais. ii. 1. p. 223. ErdmanrCs Ed. 
Locke himfelf admits " ideas of reflexion, " gained by obferv- 
ing the mind's own actions, befides " ideas of fenfation." On 
Hum. Under. 11. vi. 1. 



LAWS OF THOUGHT. 67 

account of the reprefentations of the fenfes as fuch. 
It will enumerate, for inftance, all the different kinds 
of judgments which can be formed, but will not pre- 
tend to decide upon the truth of any one judgment 
refpedting fomething which is now before the eyes. 
As the laws of the underftanding are few and inva- 
riable, whilft the phenomena in the world around us 
appear, from our imperfect knowledge of their com- 
plicated laws, very uncertain, Logic is far lefs liable 
to error than thofe fciences which have to do with 
external facts. Thus the truth that " if A is B and 
B is C, then A muft be C," cannot be denied, what- 
ever we fuppofe thefe letters to reprefent. The for- 
mula is univerfal and neceffary ; it was fo in the days 
of Ariftotle, and will be as long as there remains 
upon the face of the world one mind to think. But 
an a pojleriori fcience — a fcience of external facts — 
like Aftronomy, though ufing demonftration, depends 
upon obfervation, and the accuracy of its calculations 
is in a dire£t ratio to our opportunities of obferving 
all the circumftances which may affe£t them. It 
can never be a neceffary truth that after each inter- 
val of two hundred and twenty-three lunations the 
fun will be eclipfed \ grounded only upon fadSs, when- 
ever fome convulfion mail be prepared by the Crea- 
tor to difturb them, its predidtion will fail. Calcula- 
tions of the period of the return of comets have 



68 OUTLINE OF THE 

fometimes failed, becaufe of our defective means of 
obfervation; thus the return of the comet of 1770 
was promifed in five years and a half; it falfified the 
prediction, and never returned at all. 

This view of Logic as an a priori fcience, it is 
hoped, will meet with a pretty general aflent ; and 
we purpofely abftain from touching the great quef- 
tion of Metaphyfics — how much of our knowledge 
is from the mind itfelf and how much from experi- 
ence. The conflifting opinions upon this matter 
will never be reconciled, and perhaps the beft fervice 
which philofophy could receive would be rendered 
by marking out the region which muft be mutually 
ceded by the oppofite fchools.* 

§ 36. By explaining fome of the various names 

* Before leaving the fubje6t, it muft be noticed that the 
term a priori has undergone important changes of meaning. 
In Ariftotle's philofophy the general truth is " naturally prior" 
(wpoTspov rn <f>u<rsj) to the particular, and the caufe to the effect j 
but fince <we know the particular before the univerfal, and the 
effect before we feek the caufe, the particular and the effect are 
each " prior in refpect to us " (wporgpov Trpo? hpaq). Anal, Poft. 
1. ii. Top, vi. iv- Metaphyf. v. (a) xi. p. 1018. Ed. BeroL 
Following this, the Schoolmen call the argument which pro- 
ceeds from caufe to effect, a priori demonftration. But with 
Hume (Sceptical Doubts) a priori has the fenfe given in the 
text, which Kant has fixed in the language of philofophy. See 
Trendelenburg s Excerpta, p. 8i, Ed. in. Sir W. Hamilton's 
Reid, p. 762. 



LAWS OF THOUGHT. 69 

beftowed on Logic by thofe who have treated it, 
we fhall have a clear view of the pofition they in- 
tended it to occupy, (a.) It has been called the Ar- 
chitectonic Art, by which is meant that it occupies 
the fame pofition with regard to the fciences and 
arts in general, that Architecture does to the labours 
of the carpenter, the mafon, the paviour, the plum- 
ber and the glazier ; arranging and directing them 
indeed fo as to contribute to one common end, but 
not necefTarily knowing the details of their bufinefs, 
nor putting its hand to their toil. Ufed by Plato 
as an illuftration (Polit. 259. E.) the word Archi- 
tectonic was adopted by Ariftotle as a general name 
for all arts which kept other arts fubfervient to 
them (Etb. Nic. 1. i.). And as the rules of Logic 
muft be obeyed not by one art or the other but by 
every one, other writers were naturally led to apply 
the name Architectonic to it efpecially. — The fame 
fupremacy is vindicated to Logic in another of its 
names ; by the followers of Ariftotle it was called 
(b.) the Inftrument (or Organon) and the Inftru- 
ment of Inftruments. Ariftotle himfelf did not affix 
the name of Organon to that collection of logical 
treatifes that now bears the name ; but he fpeaks of 
our pofTeffing in ourfelves two inftruments (opyava) 
by which we can employ external inftruments, the 
hand for the body and reafon for the foul; and adds 



70 OUTLINE OF THE 

that fcience is the inftrument of reafon ; * and it is 
probable that Alexander and John Philoponus were 
led by thefe and fimilar expreffions to apply to the 
laws of reafoning, as difplayed in the two cc Analy- 
tics" of their mafter, the name of " the Inftrument," 
or Organon. Once affixed to thefe treatifes, it was 
foon extended fo as to embrace all the works that 
are now included under it. Elfewhere Ariftotle calls 
the hand of man cc an inftrument before inftruments" 
and " an inftrument of inftruments," and again com- 
pares the mind to the hand, fo that to transfer this 
compound title alfo to Logic is juft as agreeable to 
the mafter's mode of expreffion. Becaufe the rules 
of Logic are employed in every fcientific enquiry, 
Logic may well be called emphatically the inftrument 
of the mind, juft as the hand is the inftrument em- 
ployed before all others in every a£t with which the 
body is concerned. Further, juft as a hand wielding 
a fpade may be confidered an inftrument with an in- 
ftrument, fo may Logic when directing the proce- 
dure of another fcience (and where is the fcience it 
does not direft ?) be regarded as an inftrument with 
an inftrument. By its title of Architectonic we re- 
cognized Logic as the chief or mafter-fcience ; by 



* Arift. Probl. a. 5. (955 b.) De An. r. 8. (432 a 1.) Polit. 
a. 3. (1253 b.) 



LAWS OF THOUGHT. 71 

the title Inftrument of inftruments we aflfert that it 
is the fcience next and neareft to the mind itfelf, by 
which it handles, as it were, the other fciences. Some 
logicians of eminence indeed refufe to give Logic any 
other title; thus Zabarella (de Nat. Log. 1. x.) de- 
nies that it is either an Art or a Science or a Faculty 
in the proper fenfe, and affirms that the name of 
Organon is alone applicable to it. Other names 
which eftablifh the pre-eminence of Logic over the 
real fciences will not require any explanation ; fuch 
are (c.) the Art of Arts (ars- artium)^ (d.) the Syftem 
of Syftems (difciplina difciplinarum), (e.) the Key of 
Wifdom, (f.) the Head and Crown of Philofophy 
[caput et apex philofophia). But thefe fwelling titles 
muft not lead us to forget that if Logic is the higheft 
fcience of all, it is alfo the fervant of all, if it is the 
wideft in its fcope, it is alfo by itfelf the moft bare 
and fruitlefs ; it gives no knowledge of things, for it 
is an inftrumental and not a real fcience, and only 
when working in conjunction with fciences of hum- 
bler ftyle and pretenfions, can it further the interefts 
of philofophy or add to the ftock of ufeful knowledge. 
— As it offers rules for feeking after truth it has been 
called (g.) Zetetic or the Art of feeking; as thefe 
rules are not given in vain, we may regard it alfo as 
(h.) Heuriftic or the Art of difcovering truth. As it 
cures the mind of prejudices and errors, it is called 



72 OUTLINE OF THE 

(i.) Medicina Mentis and (k.) the Cathartic of the 
Mind. Logic, upon a lower view of its pretentions, 
as teaching the right ufe of the faculties in the dif- 
cuffion of any queftion, with or without the purpofe 
of attaining truth, is called (1.) Dialectic* The 
name of (m.) Canon was given by Epicurus to the 
Logic of his fchool, though, if we may truft Diogenes 
and Cicero, it was a very different fyftem from, and 
much more free from technical details than, the 
Logic in general ufe. But in the fenfe of a rule by 
which thoughts are to be gauged and meafured, to 
fecure their truth and corre£tnefs, it may be applied 
to any view of logical fcience. 

§ 37. TJfes and pretenfions of Logic. The a£ts of 
the mind are fo quick, fo numerous, fo complex, that 

* With Ariftotle, Analytic teaches the formal laws of 
thought, which philofophy applies to the difcovery of truth 5 
Dialectic (as taught in the " Topics 1 ') is a popular application 
of thefe laws, to difcuffion and the defence of a proportion, 
rather than to the attainment of truth, although it makes at- 
tempts in that direction 5 Rhetoric clofely refembles Dialectic, 
in ufmg popular forms of argument and in poftponing truth to 
fome lower aim, only that the aim of the former is to work 
conviction in the intellect, that of the latter to perfuade, 
through the intellecT: and the moral nature combined ; Sophif- 
tic is like Dialectic, except that it feeks to miflead under pre- 
tence of convincing us of a truth, and fo implies a wrong mo- 
ral bias 5 and Eriftic is the art of difputing cleverly fo as to 
put an adverfary to filence. 



LAWS OF THOUGHT. 73 

they are not eafy to note and defcribe, although we 
daily perform them, and that without ferious miftake. 
Logicians have generally erred on the fide of under- 
rating the number both of the mental procefTes them- 
felves, and of the particular aits which go to the 
attainment of any judgment or conception. As the 
act of ftanding ere£t, fo fimple apparently, calls into 
operation a numerous array of mufcles, by means of 
which the body perpetually fways and adjufts itfelf, 
without confcious effort, fo we may believe that the 
mind goes through acts, which from long practice 
fcarcely awaken her own attention, much lefs the 
fenfe of pain and effort, yet which involve a great 
number of fubordinate a£ls, depending on diftinft 
principles. And as it takes the phyfiologift many 
pages of explanation, to analyfe a poflure which a 
three-years' child affumes and retains without diffi- 
culty, fo the logician feems to fpend too many words 
upon the rules of thinking, fince all men, from the 
ftatefman to the clown, are able to think, whether 
they have learnt rules or not. To ftiow that the 
complexity we fpeak of really belongs to thoughts 
apparently very fimple, we may examine an example. 
When Captain Head was travelling acrofs the Pam- 
pas of South America, " his guide one day fuddenly 
flopped him, and, pointing high into the air, cried 
out c A lion ! ' Surprifed at fuch an exclamation, ac- 



74 OUTLINE OF THE 

companied with fuch an aft, he turned up his eyes, 
and with difficulty perceived, at an immeafurable 
height, a flight of condors foaring in circles in a par- 
ticular fpot. Beneath this fpot, far out of fight of 
himfelf or guide, lay the carcafs of a horfe, and over 
that carcafs flood, as the guide well knew, a lion, 
whom the condors were eyeing with envy from their 
airy height. The fignal of the birds was to him what 
the fight of the lion alone would have been to the 
traveller, a full affurance of its exiftence." * Here 
was an a£l of thought which coft the thinker no 
trouble, which was as eafy to him as to caft his eyes 
upward, yet which from us, unaccuftomed to the 
fubjeft, would require many fteps and fome labour. 
The fight of the condors convinced him that there 
was fome carcafs or other ; but as they kept wheel- 
ing far above it inftead of fwooping down to their 
feaft, he guefTed that fome beaft had anticipated them. 
Was it a dog or a jackal ? No ; the condors would 
not fear to drive away, or fhare with, either \ it muft 
be fome large beaft, and as lions abounded, or had 
been feen in the neighbourhood, he concluded that 
one was here. Thefe fteps of thought at leaft, and 
probably many more, rufhed through his mind with 
the proverbial fwiftnefs of thought, but they were 
fummed up in the words " A lion." Daily and 

* Sir J. HerfcheVs Prelim, Difcour/e, p. 84. 



LAWS OF THOUGHT. 75 

hourly we run through fimilar or more complicated 
trains of thinking, with no more confcioufnefs of the 
feveral links than the organ-player has of each note 
he ftrikes in a rapid paflage of full harmony. As the 
logician profeffes to give an account of the thinking 
procefs, he muft try to follow all thefe out, and fhow 
the laws on which they feverally depend. He may 
incur the charge of tedioufnefs in fhowing (for in- 
ftance) that our notion of" houfe" is formed by the 
fucceflive fteps of Comparifon, Reflection, Abftrac- 
tion and Generalization, for every one has been form- 
ing fucH general notions all his life without knowing 
one of thefe hard names ; or that " he will come, for 
he faid he would " contains three terms and three 
propofitions, joined together by a fign of inference, 
which conftitutes them a fyllogifm ; for we can all 
manage our inferences without thefe formalities. But 
ftill he muft not fhorten his explanation at the ex- 
penfe of truth ; thefe are laws of thought, and it is 
his bufinefs to afcertain them, juft as the phyfiologiPc 
thinks himfelf bound to examine all the laws of the 
bodily motions and pofitions fo unconfcioufly aflumed. 
But is there any gain to mankind from this analyfis ? 
Would not natural logic fuffice, without a number 
of technical rules, uninviting to learn, hard to re- 
member, and feldom applied? What is the ufe of 
Logic ? — I anfwer, that knowledge itfelf is a ufe, and 
that all legitimate enquiry rewards itfelf with its own 



;6 OUTLINE OF THE 

pleafures. The appetite for finding out laws from 
fads, caufes from effects, neceflary truth from fleet- 
ing occurrences of the day, puts in its claim to grati- 
fication, which is as legitimate, if lefs imperious, as 
that of the animal nature for food and fleep. The 
ftudies which enwrapt the foul of Archimedes in the 
fiege, of Aquinas at the royal feaft, of Jofeph Scali- 
ger during the maflacre of Saint Bartholomew's, muft 
have been a fource of pleafure, pure and high, from 
which they had a right to draw. If the queftion, 
what " fruit " does it bring ? — which the Baconian 
philofophy puts fo often, be underftood, as it certainly 
ought not, to refer only to the material wants and 
comforts of humanity, it is a bafe, fordid and ftupid 
queftion, againft which every better mind indignantly 
protefts. Science was never brought to its prefent 
height by hopes of wealth, plenty and comfort alone, 
but chiefly by thofe mirabiles amores with which fhe 
can infpire her followers. He who loves to fee the 
procefies of his mind reduced to their laws and caufes, 
to him are logical ftudies a pleafure — to him they 
bring fruit. 

§ 38. But whilft even the coldeft followers of Ba- 
con * admit that the value of fcience muft not be 

* See M. Comte, Philofophie, iii. p. 280, as againft the bril- 
liant but (I think) miftaken view of Bacon and the old philo- 
fophers, in Macaulafs Mifc. EJJajs. " Bacon" 



LAWS OF THOUGHT, 77 

eftimated by what (he can adtually perform, no doubt 
it muft be granted that even the higheft fciences do 
condefcend to help our loweft wants. Aftronomy, 
Chemiftry, Geology and Mechanics not only furnifh 
delightful contemplations to the ftudent, but they put 
food into the mouths of the vulgar; they clothe 
them, and fill their purfes, they put houfes over their 
heads, and adorn them with obje£ts of beauty and 
convenience. Logic has its ufe alfo in improving the 
condition of men ; it teaches, or perhaps I may only 
fay, may be made to teach, them to think. This is 
often denied, and partly on account of the extrava- 
gant claims put forward by logicians, w T ho affume 
that the acquifition of a few logical rules will enable 
men to think corre£Hy, juft as the pofleffion of a 
watch enables them to afcertain the hour. No fci- 
ence can make fuch pretenfions. The a£Hve intellect 
has two parts, one of which originates our thoughts, 
and may be called the fuggeftive, whilft the other 
checks and judges thoughts as they arife, and may be 
called the critical, power. Thoughts are continually 
fuggefted without the confent of the will. One would 
think indeed, were it not for the obvious fimilarity 
thefe fpontaneous vifitors bear to the matter of for- 
mer ftudy, that they were in no fenfe our own, that 
an independent being, over whom one had abfolutely 
no control, was whifpering within us. In the poeti- 



78 OUTLINE OF THE 

cal temperament, where the power of fuggeftion 
ftrongly predominates, the thoughts which arife are 
lefs like any thing one remembers, than in ordinary 
minds ; and hence poets have maintained, perhaps in 
full fincerity, that an unfeen fpiritual power, higher 
than themfelves, ufed them as the channel of its 
teaching, — that they were infpired.* The fuggeftive 
power may be educated as certainly as, though more 
gradually than, the critical. The difcovery which 
we call a flafh of genius, a happy thought, really de- 
pends as much upon previous acquirements, as the 
power of ftating a cafe or applying a rule does. Thefe 
bright fuggeftions never occur to the ignorant ;f they 
have the fa£ls before them, but their imaginations 
are not trained to leap to the proper inference from 
them. All difcipline of the fuggeftive muft proceed 

* Plato again and again mentions this claim of poets. See 
Ion y 533, D. Apol. Soc. 22, B. C. Legg. 719, C. Me/20. 99, B. 
C. Phadrus, 245, A. Stallbaum {Preface to Ion) does not think 
that Plato would deny to the poet a modifying power over the 
dictating principle. But the truth is, Plato ftill allows them 
all they claim, in order that the want of independence (alro- 
irpayU) may be feen and defpifed. Compare Ovid. (Fafti. vi. 
5) Cicero {de Di<v. i. 37). Morgenflern {de Rep. p. 296). Dic- 
tation and infpiration are diftinguifhed, Coleridge 's Table Tatt, 
ii. 30. 

f See this beautifully illuftrated in Whe^well^ Phil. Ind. Sci. 
B. xi. § 5. And below, the feclion on Anticipation. 



LAWS OF THOUGHT. 79 

from the critical power ; it is by a long, careful, pa- 
tient analyfis of the reafonings by which others have 
attained their refults, that we learn to think more 
correftly ourfelves. He who reads over a work upon 
Logic probably thinks no better when he rifes up 
that when he fat down ; but if any of the principles 
there unfolded cleave to his memory, and he after- 
wards, perhaps unconfcioufly, fhapes and corrects 
his thoughts by them, no doubt his whole powers of 
reafoning gradually receive benefit. Perhaps the prin- 
cipal advantage which fcience has received from Ba- 
con's great work, has arifen from his denouncement 
of hafty generalization, 5 * which being eafily remem- 
bered, and applicable to all fubje&s, has much influ- 
enced the pra&ice of all fcientific ftudents. In a 
word, every art, from Reafoning down to Riding and 
Rowing, is learnt by afliduous pradtice, and if prin- 
ciples do any good, it is proportioned to the readinefs 
with which they can be converted into rules, and the 
patient conftancy with which they are applied in all 
our attempts to excel. 

§ 39. No one will pretend to fay that Logic has 
been fairly treated in this refpeft. Our view of the 

* Nov. Organ. I. 19. 20. 22. Not that Bacon firft difco- 
vered this abufe of the law of Anticipation. Plato knew it 
well enough, {Pkilebus. 16. e. q\ tiz vvv a. t. x.), and has ftated 
it almoft in the fame way. 



80 OUTLINE OF THE 

elements of Logic has indeed been very imperfect, 
and would be quite infufficient for fcientific analyfis ; 
but no attempt has been made to widen and improve 
it, becaufe we have not tried to put it to ufe, and fo 
found out its inadequacy. In fome popular treatifes, 
of lateft date, both Englifh and French, the rules of 
fyllogifm are paffed lightly over, as rufty weapons 
that have no place in the armory of fcience — " You 
will find them fomewhere — in Ariftotle, in the School- 
men, or in Manuals — we admit their exiftence, but 
to teach them is befide our purpofe — we prefent you 
only with a fmall fpecimen or two for curiofity's 
fake." This courfe is to us unintelligible. The rules 
in queftion claim to be thofe which regulate the act 
of reafoning ; if a fyftem profeffes to teach reafoning, 
it fhould either give us the rules complete, or prove 
that they are falfe or defective. A large book on 
Logic that refers us to another book for the rules of 
the great logical act, does not fulfil its duty ; and fug- 
gefts a fufpicion that thefe rules have not been made 
ufe of as the inftrument of fcientific refearch — that 
proper trouble has not been taken to afcertain how 
far they are really applicable to fuch a purpofe, and 
how far abfurd and ufelefs. I believe that if a fet of 
rules, as free from technicalities of form and expref- 
fion as is confiftent with complete accuracy, be fe- 
duloufly applied to the examination of the books we 



LAWS OF THOUGHT. 81 

read, more efpecially to the hiftory and theory of 
fome particular fcience, the mind will receive great 
and fignal benefit, and the creative powers will be 
increafed as well as the judgment ftrengthened. In 
paft days it was worth while to learn the fcholaftic 
terminology, becaufe it ran through all fcientific prac- 
tice ; the theology and metaphyfics of Aquinas and 
Occham vindicate their right to fpend time upon the 
barbarifms of their Logic. Let us get by degrees a 
logic which is to our philofophy, what that of the 
Schoolmen was to theirs, and no one will complain 
that fome of its expreffions are technical and its rules 
hard to underftand. Technicalities are only weari- 
fome, where we have no hope of their after-fruits to 
lure us through them. 

On thefe grounds, we try to make the analyfis of 
thinking as complete as poffible, and beg the ftudent 
to mafter a few new names, expecting that the trou- 
ble fo beftowed will not be grudged as a preparation 
for that habitual examination of thoughts and argu- 
ments which is the great means of teaching us to 
reafon. For, the rules of Logic, thofe of fyllogifm 
for example, do not teach a new trick of argument, 
nor furnifh an inftrument by the pofTeffion of which 
we are at once enabled to fpeak or difpute. There 
is neither trick nor magic in them ; they are princi- 
ples which we call into ufe every hour of our lives. 

G 



82 OUTLINE OF THE 

They do not impart any new faculty, but lay bare 
before us the nature of that reafoning which has been 
from childhood our delight and our prerogative. Who 
mall fay that this is a frivolous or unworthy ftudy ? 

§ 40. But it is thought advifable that young men 
who are not inclined to examine with habitual pa- 
tience their own thoughts or the procedure in any of 
the real fciences, mould acquire fome flight know- 
ledge of Logic. In this cafe, we cannot expe£t the 
fame diligence in learning technical terms and rules, 
as they will not be required hereafter. The difficul- 
ties of mode and figure will be reluitantly mattered, 
becaufe in popular language no one mentions them. 
But what is the courfe adopted ? We attenuate the 
fqience, where we ought to Amplify it ; we reduce 
the fize of our manuals in the vain hope of leflening 
their difficulty : and there remains little more than a 
catalogue of hard terms with harder explanations — 
little elfe than a reliquary of the dry bones of that 
fyftem of knowledge which five hundred years ago 
was alive and breathing. No wonder that untrained 
minds are repelled. Inftead of explanation and il- 
luftration of common things, they find the plaineft 
and fimpleft veiled behind the terms of a forgotten 
metaphyfical fyftem ; they are commanded to maf- 
ter all the rules required for an extenfive practice of 
logic, though they never mean to enter upon fuch 



LAWS OF THOUGHT. 83 

a courfe, and are not encouraged to do fo now, ex- 
cept by the moft puerile examples. Surely it is not 
worth their while to learn the language of a region 
of philofophy in which they are never to travel. 
Surely it would be poffible to give them fome found 
and accurate inftru&ion in the nature of their thoughts 
and minds, making ufe only of the language of com- 
mon life. Every art and fcience has the right to 
form its own terms ; but neceffity can alone juftify 
the exercife of it. New fa£ts and laws require new 
words, but he who hides a well-known thing by a 
ftrange name, makes truth ridiculous by the robe of 
mock dignity he clothes her with. Only in the hope 
that the nomenclature of logic which the following 
pages contain may become familiar by a fteady courfe 
of logical practice, do I invite my reader to mafter 
it. But where there is to be no practical application 
of the rules, it would be advifable to ftudy fome po- 
pular work, in which the leading principles only of 
mental or phyfical fcience are familiarly expounded. 
A book like Sir J. HerfchePs Preliminary Difcourfe 
on Natural Philofophy carefully read will do more to 
expand the mind than years of toilfome ftudy of the 
technical rules of thought, purfued without that prac- 
tice of logical analyfis which is its natural comple- 
ment. 

§ 41. In the divifion of the fubje&, I fee no caufe 



84 OUTLINE OF THE 

to deviate materially from the ordinary diftribution 
into three parts, the firft treating of Conception, or 
the power of forming general notions, the fecond of 
Judgment, or the power of deciding whether two 
notions agree or not ; and the third of Syllogifm, or 
the power of drawing one judgment from another.* 
To thefe a fourth part, in which Method, or the 
power of ufing the other three functions in the dif- 
covery of truth, is explained, has been ufually added ; 
which anfwers to the applied Logic of the prefent 
work. But it is proper to notice one or two objec- 
tions to this divifion. 

§ 42. In beginning with conceptions, we are 
charged with putting the laft, firft. Men cannot get 
a clear conception without paffing a judgment about 
it ; nor can they always pafs a judgment without cer- 
tain reafonings, or fyllogifms \ fo that we go to the 
third part of Logic to eftablifh what belongs to the 
fecond, in order that from that we may more clearly 
underftand fomething which relates to the firft. Why 
not begin then with the third ? 

Whilft this regreffive order is certainly natural, 
and whilft a Logic might be written which fet out 
from the fentence or the fyllogifm, and analyfed it 

* Another divifion has been adopted from Porphyry (Ifag. 
1. 1) by fome logicians, who confider Logic as the fcience of 
defining, dividing, and arguing. 



LAWS OF THOUGHT. 85 

into judgments, and thefe again into conceptions ; the 
contrary procedure, from the fimpleft element of rea- 
foning, the conception, to the fyllogifm which is its 
complete ail, will be found in our opinion eafier to 
follow. The analyfis has long fince been performed, 
and we find it convenient to proceed by fynthefis, in 
this as in many other fciences. But the objection is 
valuable, as bringing out the contraft between the 
natural courfe of reafoning and its technical expla- 
nation. Why do we reafon ? To find whether fome 
judgment, which has fuggefted itfelf to our minds, be 
true or not. Why do we feek to make this judg- 
ment ? To add fomething to the clearnefs of the no- 
tion that is its fubje£h Copernicus reafoned to prove 
that the globe revolved round the fun ; and he eftab- 
lifhed this judgment that when men thought of " the 
globe" in future they might know it as " the revolv- 
ing globe." All the reafonings in Ariftotle's Ethics 
are to give a more adequate notion of happinefs ; — 
of Plato's Republic, to improve our notion of juftice; 
— of Bacon's Organon, to afford a more accurate 
conception of Method. 

§ 43. Another objection againft the divifion is that 
it diftinguifties parts which are really confufed ;* that, 
for example, when we divide fuch a conception as 

* D amir on, Logique, p. 4. 



86 OUTLINE OF THE 

that of "gafes" into inflammable and non-inflamma- 
ble, we really pafs a judgment, though we explain 
divifion in the firft part of Logic, which treats of 
Conception. 

The anfwer to this may be fuggefted by that to 
the preceding one. We do not deny that the pro- 
ceffes of the mind run into one another, that a man 
judges when he forms conceptions, and fo on ; we 
only afk for leave to defer ibe each procefs feparately. 
Our arrangement is confefledly artificial. 

§ 44. Some logicians indeed argue that properly 
fpeaking Judgment is no diftinft a£t of thought, but 
rather a part and condition of every aft. Every no- 
tion feems to imply a judgment ; when I think of 
the Queen, gravitation, or virtue, I mean that the 
Queen — gravitation — virtue exijis ; fo that we have 
one common attribute which we affirm of every 
thing, that of exiftence. But it is one thing to fay 
that a judgment may be, and another that it zV, made. 
Before the component parts of any complex notion 
could be brought together in the mind, many judg- 
ments muft have been paflfed \ but when the notion 
recurs, we do not furely pafs the judgment over 
again. My notion of freedom implies that it is the 
ftate of being able to do as I will, having refped: 
however to the rights of others, and that this is a 
ftate poflible for men ; but I do not formally affirm 



LAWS OF THOUGHT. 87 

either that it contains thefe attributes or that it is pof- 
fible, and therefore my mentioning freedom involves 
no judgment, although I may if I pleafe form judg- 
ments about it. We muft carefully diftinguifh be- 
tween a pofiible and an a&ual judgment — between a 
notion which is and one which may be the fubjeft of 
a judgment. 

§ 45. Method, which is ufually defcribed as the 
fourth part of Logic, is rather a complete practical 
Logic. Whilft the other three parts defcribe each a 
diftin£t and complete product of thought, the Con- 
ception, the Judgment, and the Syllogifm, no fuch 
whole is treated of in the do£trine of Method ; which 
may be ufed for making a whole fcience, or a whole 
fpeech, a fyftem or a fentence. Method is rather a 
power or fpirit of the intellect, pervading all that it 
does, than its tangible product.* Hence we put in 
the place of rules for Method as a part of Logic, an 
Applied Logic, which mows under what conditions 
in the feveral regions of enquiry the three a£ts of 
thought may be fafely performed ; and how far rules 
can avail to direct the mind in the ufe of them to 
profitable or beautiful refults. 

§ 46. The attempt to apply the rules of Logic 
will both raife and lower the opinion which obtains 

* See the fragment on Method in Coleridge' 's Friend, vol. iii. 



88 OUTLINE OF THE 

concerning the worth of the fcience. Thofe who 
condemn it altogether, as arbitrary and artificial, as a 
fet of rules for arguing, put together in an age when 
truth was lefs the objecSl of defire than argument, 
may find to their furprife that it is only a fearching 
and fyflematic account of procefles which they daily 
perform, whether in thought, or in argument, in the 
purfuit of a fcience or in the tranfadtions of the ftreet 
and market. Thofe on the other hand who expeft 
that Logic will be to them a golden key to unlock the 
treafure houfe of the knowledge of the univerfe, will 
find that it neither gives them nor pretends to give, 
any new power ; that it only refines and ftrengthens 
powers they already poflefs ; that out of a dunce it 
never yet made a philofopher. Whilft its rules apply 
to every fcience, and it may therefore lay fome claim 
to its ancient titles — the Art of Arts, the Inftrument 
of Inftruments — it only affifts us in the ftudy of the 
fciences, not ftands in their ftead. We muft fight 
our own way over every inch of ground in the field ; 
but Logic will often prevent our throwing away our 
blows. She can do no more. Sophifts of Greece 
may offer to teach us " a trick worth a hundred 
minae," which is to be the fecret of all wifdom ; or 
Lully and Bruno may pretend fo to arrange in tables 
the refults of human refearch that a child may know 
where to put his hand on the moft recondite fecrets, 



LAWS OF THOUGHT. 89 

and employ them at pleafure. But thefe are wild 
dreams of the infants of fcience, which thinkers in 
their fober, waking moments hardly mention but with 
a fmile. We only affirm that when men think, thefe 
are the rules according to which their thoughts run, 
that the knowledge of laws and principles, indepen- 
dent of ulterior profit, is always gratifying to active 
minds, and that inafmuch as the clear underftanding 
of what is right, is always ufeful for the avoidance of 
what is wrong, Logic is an ufeful inftrument in think- 
ing. But it gives us the forms of knowledge, not the 
matter. It will not lay bare the hidden fprings of 
moral action ; nor explain the myftery of life, of fleep, 
of fancy, of memory ; nor difplay the future deftina- 
tion of man and the world. Still lefs will it be to us 
inftead of eyes, if, turning away from this ball of 
earth on which we ftand, we try to look off" to the 
Infinite — the Abfolute — the Eternal, whofe nature 
will not take the mould of our intellectual forms, 
who comprehends us, when we vainly think that we 
comprehend Him. 



OUTLINE OF THE LAWS 
OF THOUGHT. 

PART I. 
CONCEPTIONS. 

" Non obftant hae difciplinae per eas euntibus, fed circa illas 
haerentibus." 

QUINCTILIAN. 




CONCEPTIONS. 

§ 47. Cognitions in General. 

? HE want of any manual of Metaphyfics 
to which we might conveniently refer, 
compels us to explain here the names 
of the fimpleft mental impreffions, in as 
far as Logic prefuppofes the poiTeffion of them. 

The impreffion which any object makes upon the 
mind may be called a Prefentation. Some Prefenta- 
tions are admitted into the mind without being no- 
ticed, as is the cafe with the words fpoken to a dreamy 
or abfent man, or with a houfe or tree which, form- 
ing part of a great landfcape, efcapes the fpecial no- 
tice of the beholder. The mind is unconfcious of 
them - 9 it fees or hears, but does not know that it fees 
or hears, fo that the impreffion is not clear. And yet 
it is a real impreffion, becaufe when attention is di- 
rected to it, we know that it muft have been there 
before. A man ftares his friend in the face without 
recognizing him ; when his friend awakens his atten- 



94 OUTLINE OF THE 

tion, the recognition takes place. But he knows that 
it is not the impreffion upon his eye which begins at 
that point of time, but his attention to the impreffion. 
Prefentations then are divided into Clear and Ob- 
fcure, and the former, with which alone Logic is 
concerned, may be called Notions or Cognitions. 

Clear Prefentations, or Cognitions, are fubdivided 
into confufed and diftin£t. Where the marks or at- 
tributes which make up the Prefentation cannot be 
diftinguiftied, it is confufed j where they can be dif- 
tinguifhed and enumerated, it is diftinft. For ex- 
ample, we have a clear notion of the colour red ; but 
we cannot tell by what marks we identify it, we 
could not defcribe it intelligibly to another, and hence 
our cognition of it is confufed ; again, we have a 
clear notion of houfe, but we can declare its various 
marks, namely, that it is an enclofed and covered 
building fit for habitation ; and therefore our notion 
is diftin£t. 

We fubdivide the clafs of diftinft notions twice, 
according to two principles of divifion ; and firft, into 
adequate and inadequate notions. Adequate notions 
are thofe in which, befides enumerating the marks, 
we can explain them ; that is, can enumerate the 
marks of the marks of the diftinct notion, and again 
the marks of thofe marks. As this kind of analyfis 
is almoft interminable, we call a notion adequate, not 



LAWS OF THOUGHT. 95 

when the enumeration of fubordinate marks has been 
carried to the fartheft, but when they have been enu- 
merated fufficiently for our prefent purpofe, in what- 
ever fubject we are employed. Our notion of hap- 
pinefs, for inftance, (according to Ariftotle) is ade- 
quate, when we not only know that it is " an energy 
of the foul according to the beft virtue, in a complete 
life ; M but can explain what we mean by an energy 
of the foul, the beft virtue, and a complete life. So 
we have an adequate notion of what Hobbs means 
by Right, when we not only know that it is " unre- 
fiftible might in a ftate of nature," but can explain 
what unrefiftible might and ftate of nature are. The 
fame two notions would be inadequate, if we had the 
refped-tive definitions of them, but could not explain 
them. 

The other divifion of diftinct notions is into fym- 
bolical and notative ; it has been already explained.* 

TABLE OF NOTIONS. 

{Confufed. r 
Adequate 
Diftinft J l Inadec l uate 
I J Symbolical 
I Notative. 

* P. 45, feq. Throughout this feclion we have followed 
Leibniz,, with fome flight alterations. See Erdmantfs Leibniz,, 



96 OUTLINE OF THE 

§ 48. Intuitions and Conceptions. 

The notions formed in the mind from things of- 
fered to it, are either of fingle objects, as of " this 
pain, that man, Weftminfter Abbey :" or of many 
objects gathered into one, as " pain, man, abbey." 
Notions of fingle obje£ls are called Intuitions, as 
being fuch as the mind receives when it fimply at- 
tends to or infpeits (intuetur) the obje£t. They are 
alfo called Singular Reprefentations. Notions formed 
from feveral objects are called Conceptions, as being 
produced by the power which the mind poflefles of 
taking feveral things together (concipere i. e. capere 



p. 79. Ada Erudit. an. 1684, Some ufeful diftin&ions in the 
various names of notions, are given by S. T. Coleridge. 

" The moll general term (genus fummum) belonging to the 
fpeculative intellect, as diftinguifhed from acts of the will, is 
Reprefentation, or (ftill better) Prefentation. 

" A confcious Prefentation, if it refers exclufively to the 
fubje6t, as a modification of his own ftate of being, is=Senfa- 
tion. 

" The fame if it refers to an object, is=Perception. 

" A Perception immediate and individual is=an Intuition. 

" The fame Mediate, and by means of a character or mark 
common to feveral things is— a Conception. 

" A Conception, extrinfic and fenfuous, is=a Fact or a 
Cognition. 

" The fame purely mental and abftracted from the forms of 
the underftanding itfelf is=a Notion." Church and State> p. 
301. 



LAWS OF THOUGHT. 97 

hoc cum illo) according to the principle to be explained 
prefently. They are alfo called General Notions or 
Reprefentations. 

§ 49. Formation of Conceptions. 

On a firft infpection of an object of an entirely 
novel kind, we are unable to diftinguifh between its 
eflential and accidental properties, between what it 
muft always exhibit and what it might difpenfe with. 
A perfon who had lived all his life on the fhore of 
the Atlantic, would believe, unlefs otherwife inform- 
ed, that every other fea refembled this in all particu- 
lars, in its tidal movement, though the Mediterranean 
is almoft tidelefs, in its degree of faltnefs, though the 
tafte of the Dead Sea is much more bitter and its 
compofition different, and fo on. In travelling, or in 
reading a book of travels, he is made acquainted with 
another fea with properties not quite identical indeed, 
but ftill fo far fimilar that he cannot help regarding the 
new fpecimen as of the fame kind as the old. This 
he fees at once upon making the comparifon of the 
two objects ; and he then proceeds to reflect upon 
the properties of each, with a view to difcover the 
points in which they agree, as well as thofe in which 
they are at variance. Having afcertained what they 
are, he fees that a feparation muft be made between 
the difpenfable and the indifpenfable properties^ be- 

H 



98 OUTLINE OF THE 

caufe the latter will belong to each and every fpeci- 
men of this kind, whilft the former, as he now fees, 
need not be prefent to conftitute a fea what it is. He 
proceeds then to abftra£t, or draw off* (abftrahere), 
the points in which feas are to agree from thofe in 
which they may differ ; and the properties fo drawn 
off and kept apart, are called the Notes or Marks or 
Attributes of a fea, and form when taken together a 
Univerfal or Common Nature (Univerfale). But he 
cannot think of a common nature without implying 
a clafs of things, be the number large or fmall, in 
each of which this fet of attributes is to be found, 
and each of which muft exhibit them as its creden- 
tials for admiffion into the clafs ; in taking this fur- 
ther ftep he generalizes, or forms a Genus or Clafs, 
Laftly, as he cannot be fure of remembering the clafs, 
nor hope to recall it to the minds of others who have 
gone through, or who at leaft take for granted, the 
fame fteps of thought, without a name to reprefent 
it, he , either invents a new name, or applies that by 
which he once defignated a fingle thing, to the whole 
clafs ; which is an aft of Denomination. 

There are here no lefs than five fteps, which muft 
have been taken by every one who fully and fairly 
realizes a general notion, and fome of which muft 
have been made even by thofe who have a lefs dif- 
tin£t apprehenfion of what they mean when they 



LAWS OF THOUGHT. 99 

fpeak of clafTes. i. Companion is the act of putting 
together two or more fingle objects with a view to 
afcertain how far they refemble each other, ii. Re- 
flection is afcertainment of their points of refemblance 
and their points of difference, iii. Abftraction is the 
feparation of the points of agreement from thofe of 
difference, that they may conftitute a new nature, 
different from, yet including, the fingle objects, iv. 
Generalization is the recognition of a clafs of things, 
each of which is found to poffefs the abftra&ed 
marks, v. Denomination is the impofition of a name 
that mail ferve to recall equally the Genus or Clafs, 
and the Common Nature. 

The procefs thus analyzed into five acts is often 
defcribed generally by the principal of them, as Ab- 
ftraction ; and for convenience' fake that word fhall 
be reckoned fufficient here. 

§ 50. Higher and Lower Conceptions. 

The functions of Abftraction do not ceafe as foon 
as we have compared feveral intuitions, to form one 
conception. We may proceed to form a larger con- 
ception from feveral narrower ones ; and this too is 
done by Abftraction. By obferving John, Thomas, 
and Peter, and abftradting from their accidents the 
effential marks, we get the notion of man ; but again, 
by comparing the conception man with other con- 



ioo OUTLINE OF THE 

ceptions, cow, fheep, wolf, whale, and obferving the 
mark common to all, that they fuckle their young, 
we form the wider conception Mammalia, — wider, 
becaufe it includes man and many other conceptions. 
We may carry the procefs farther ftill ; and, with 
writers on Natural Hiftory, compare the Mammalia, 
with Aves, Amphibia, Pifces, Infeftae, and Vermes, 
when we mail difcover that all thefe, however dif- 
ferent, agree in having life and fenfation, from which 
marks we gain the new conception animal, wider 
than any of the former, as including them all, — 
higher, as requiring a fecond ftep in the abftra£tive 
procefs to reach it. 

§ 51. Genus , Species ^ Individual. 

In this fcale, compofed of more or fewer fteps, the 
loweft is always the intuition or Individual. The 
next is called the Loweft Species, [infima fpecies) 
which can only contain fingle objects, not fubordi- 
nate kinds or claffes. All the higher rounds of 
the ladder, except the higheft, are called Subaltern 
(fubalterna) Genera, which are alternately genera 
and fpecies, genera to the lower, and fpecies to the 
higher and wider conceptions. The wideft clafs, 
with which Abftra&ion ceafes, is called the Higheft 
(fummum) Genus, becaufe in this hierarchy of con- 
ceptions it is not brought under any other genus as 



LAWS OF THOUGHT. 101 

its fpecies, but is itfelf the genus to each conception 
in the feries. Thus the 

Individual is neither genus nor fpecies. 

Infima Species is never a genus. 

Summum Genus is never a fpecies. 

Subalterna Genera are genera to thofe below them, 
and fpecies to thofe above. # 

A feries of this kind, in which the fame individuals 
are found throughout, is called a fyftem of cognate 
genera. Thus, in the feries Socrates, Philofopher, 
Man, Animal, the fame individual, Socrates, is found 
in each of the three conceptions, and might have 
the name of it applied to him. 

It muft be remarked that the Summum Genus and 
the Infima Species are fixed fomewhat arbitrarily. 
There can only be one abfolute fummum genus, and 
we may go on abftrafting until we come to fome 
wide notion, be it " thing" or "fubftance" or " ef- 
knce" or "object," that comprehends all that we 
can think about. If we flop fhort of this, as the 
Naturalift does when he makes Animal his higheft 
genus, the name can only be ufed in a qualified fenfe, 
and our genus is only the higheft becaufe we will 



* With the Greek Logicians the Summum Genus is yiv.q 
ymnobTa,7ov, the Infima Species, e?$os Blhuwrarov, the fubaltern 

genilS, E&og fxia-ov xcu VTta.XKn'kov. 



102 OUTLINE OF THE 

make it fo. Then, we can fcarcely ever afcertain 
the infima fpecieS) or that kind that is too narrow to 
be divided into other kinds, becaufe even in a hand- 
ful of individuals we cannot fay with certainty that 
there are no diftinftions upon which a further fub- 
divifion into claffes might be founded. 

The genus next above a given fpecies is called 
proximate ; thofe that are ftill higher are called re- 
mote. A number of fpecies that have the fame proxi- 
mate genus are faid to be co-ordinate. 

§ 52. Marks or Attributes. 

Thofe properties by which we recognize any ob- 
ject, and affign it a place under fome appropriate 
conception, are called its marks. If thefe are inva- 
riably found in the objects of a given fort, they are 
called eflential ; if only a portion of the clafs poflefles 
them, they are accidental. The whole of the eflen- 
tial marks of a fpecies make up its fpecific character, 
or its eflence. Two marks which are in the very 
mode of exprefling them oppofed to each other, as 
wife and unwife, mortal and immortal, are called 
contradictory, becaufe it is impoffible to affign them 
to the fame obje£t without a contradiction in terms ; 
and this is certain a priori^ becaufe the one is the 
mere negation of the other, fo that their oppofition 
does not depend on an examination into the nature 



LAWS OF THOUGHT. 103 

of thefe marks. If they were reprefented as A and 
not-A, we mould be as fure that they were diame- 
trically oppofed, as if A was a word of well-known 
meaning, inftead of an arbitrary fymbol. Marks 
which are oppofed to each other, but not as a pofi- 
tive and negative, fo that we know their contrariety 
a posteriorly from experience, as fweet and four, hard 
and fluid, are termed repugnant marks. Thofe which 
may meet in the fame object, as fweet and fluid, 
four and hard, we may call compatible. 

§ 53. Extenfion and Intenfion. 

When we compare a vague and general concep- 
tion with a narrower and more definite one, we find 
that the former contains far more objects in it than 
the latter. Comparing plant with geranium, for ex- 
ample, we fee that plant includes ten thoufand times 
more objects, fince the oak, and fir, and lichen, and 
rofe, and countlefs others, including geranium itfelf, 
are implied in it. This capacity of a conception we 
call its extenfion. The extenfion of plant is greater 
than that of geranium^ becaufe it includes more ob- 
jects.* 

* Mr. Mill, Logic, I. vii. i, thinks it only " accidental'" 
that " general names 1 ' mould be the names of clafTes. But his 
own language contradicts him ; if they are general they belong 
to genera ; it cannot be accidental that a clafs-name mould be 
the name of a clafs. 



io4 OUTLINE OF THE 



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LAWS OF THOUGHT. 105 

But conceptions have another capacity. Whilft 
plant has more objects under it than geranium, it 
has fewer marks in it. I can defcribe the leaves, 
petals, ftamina, and piftils of geranium ; but of plant 
no fuch defcription is poffible. I cannot fay that 
every plant has a ftem, for there are the lichens to 
contradict me \ nor a flower, for ferns have none, 
and fo on. I can fay little more about plant, than 
that all plants have growth and vegetable life. The 
logical expreffion of this defecl: is, that its intenfion 
is very limited. 

The greater the extenfion, the lefs the intenfion ; 
the more objects a conception embraces, the more 
(lender the knowledge which it conveys of any of 
thofe objects ; and vice verfd, % 

With the help of the important diftinc~tion be- 
tween extenfion and intenfion, or as others exprefs 



* The various modes of expreffing the double capacity of 
conceptions, which has been called by Sir William Hamilton 
" the cardinal point of Logic/ 1 are as follows. 
A conception viewed as a 



Logical whole 


Metaphyfical whole 


has 


has 


Extenfion 


Intenfion or Comprehenfion 


Breadth 


Depth 


Sphere 


Matter 


Objects 


Marks 


Power to denote. 


Power to connote. 



106 OUTLINE OF THE 

it, the fphere and matter of the conception, magni- 
tudo et vis conceptus^ we can underftand the meaning 
of the faying — that the fubje£t of a judgment is in 
the predicate, and the predicate in the fubje£t. " Man 
is an animal ;" this conveys two notions, that man 
is contained in animal, as a fpecies in a genus ; and 
that whatever makes up our notion of animal — all 
the marks of animal — are contained in (v7rdgxei *) 
man. So they are mutually contained. 

§ 54. Determination. 

The reverfe of the abftradtive procefs, that of de- 
fending from higher conceptions to lower, by re- 
fuming the marks laid afide, is called determination. 
Thus from the broad clafs of difeafes, we determine 
or mark out the clafs of fevers, by the peculiar fymp- 
toms of heat, rapid pulfe, &c, which are their marks ; 
and from fevers we defcend further to intermittent 
fevers, by bringing in the frefli mark of time. 

As abftradtion augments the extenfion by dimi- 
nifhing the marks, fo determination augments the 
intenfion by increafing them. Notions of individuals, 
and they only, are faid to be fully determined, be- 



* 



Ariftotle (Anal. Pri. I. i. and many other places) adopts 
in preference this mode of putting the proportion. Inftead of 
" Man is an animal/' he has " Animal inheres in man." 



LAWS OF THOUGHT. 107 

caufe to them there are no more marks to add. The 
ufe of the word determination in its logical fenfe is 
already fanftioned by our older writers. 

§ 55. Privative Conceptions. 

Befides conceptions which are formed from marks, 
there are others formed from the privation or ab fence 
of marks. Our notion of kindnefs arifes from fome 
marks which a kind perfon always exhibits ; but 
whence our notion of its oppofite unkindnefs ? From 
the want of the marks, whatever they may be, of 
kindnefs. So too, in marking by a name any clafs 
-of objects, as animal or ftone, we neceffarily imply 
that there are correfponding clafTes, which are not 
animals and not Jlones ; about which, it is true, we 
know very little, as we can only fay what they are 
not. Any pair of conceptions, a pofitive and a pri- 
vative, muft, fpeaking abfolutely, divide the whole 
univerfe. Either in man or in not-man, all objects 
muft be found, — ftar, flower, form of government, 
or moral quality. But practically we limit this ab- 
folute divifion. We never think, for inftance, of in- 
cluding an oak-tree among the number of things that 
are not kind, though undoubtedly it does lack the 
marks of kindnefs. It is more convenient to think 
of fuch a pair of conceptions as kind and not-kind, 
not as dividing between them the whole univerfe, 



io8 OUTLINE OF THE 

but only fome wider conception, as moral-beings. 
So that we mean to include in our notion of unkind, 
not every thing which is unkind, but every moral 
being that is fo. Such a larger conception, which a 
pofitive and privative divide between them, may be 
called the fecond fphere of the pofitive. # 

§ 56. The three powers of a Conception. 

That all fimple cognitions have three powers or a 
threefold value, in that they confift of marks, and 
include objects, and are fummed up in names, has 
been ftated already. To thefe three functions as 
many procefTes correfppnd; Divifion of a Conception 
enumerates all the objefts or claffes that are included 
under it, and fo deals with the extent of the notion ; 
Definition expounds all the marks implied in the 
notion, and fo reprefents to us the nature or fpecific 
character of it ; and Denomination, and Explanation 
of Names, affix the verbal fign to a conception, and 
interpret given verbal figns already in ufe, fo that 
they may be referred to the notions they really re- 

* The bzvTEpa, ova-la of Ariftotle (Categ. ch. v.) mayjuftify 
the term fecond fphere \ ProfefTor De Morgan propofes to call 
it the univerfe of the pofitive conception. The privative has 
been called by fome the contradictory, by others the contrary, 
of the pofitive. But either expreflion tends to confound con- 
ceptions with judgments. 



LAWS OF THOUGHT. 109 

prefent, and to no others. The nature of thefe pro- 
ceffes muft be explained more in detail. 

§ 57. Logical Divijion. 

Divifion is the enumeration of the various co-or- 
dinate fpecies of which a proximate genus is com- 
pofed. The rules for conducting this procefs cor- 
rectly are 

i. The conftituent fpecies, called the dividing mem- 
bers [membra dividentia) muft exclude one another. 

ii. The conftituent fpecies muft be equal, together, 
to the genus divided (divifum). 

iii. The divifion muft be made according to one 
principle or ground (fundamentum diviftonis). 

The reafon of thefe rules, and of the terms of the 
explanation of Divifion, will be apparent v/hen the 
ufes to which the procefs was intended to minifter, 
are fairly confidered, and thefe, although they belong 
rather to applied Logic, may be introduced here. 
The treatment of a fubject is greatly facilitated by an 
orderly arrangement of its feveral parts. If Natural 
Hiftory, for example, were to go no further than its 
name feems to require, if it were a mere collection 
of curious information about natural products, with- 
out order and completenefs, no memory would be 
able to mafter its details. Omiffions would detract 
from its value; and repetitions would difguft the 



no OUTLINE OF THE 

ftudent. But it maps out the kingdom of nature into 
great diftri£ts, and fubdivides thefe into fmaller por- 
tions, fo as to fecure us from ferious omiffions, to 
preclude confufion, and to affift the memory; and 
fo becomes worthy of the name of a fcience. The 
firft rule then, as given above, is to fecure that the 
claffes and fubclafles fhall be diftinft from each other, 
that they fhall not overlap each other, or be what 
Leibniz calls communicant fpecies. Exceptions to 
this rule are often unavoidable, efpecially in fubje£ts 
that do not belong to ftri£t fcience : thus, in enume- 
rating the fpecies of imaginative writers, one would 
probably mention poets, dramatifts, and writers of 
tales ; yet fome poets are dramatifts, and fome tales 
are poems. The fecond rule provides that no clafs 
fhall be omitted, and fecures completenefs. The 
principle of divifion mentioned in the third rule is 
fome new conception, for the marks of which we 
feek in the conception to be divided. Thus man 
may be divided into European, African, Afiatic, 
American, and Auftralian ; and again into Chriftian, 
Mohammedan, Jew, and Pagan, and again into juft 
and unjuft \ and in the firft divifion locality, in the 
fecond religion, and in the third behaviour, is the 
principle of divifion.* Now as it is impoftible to 

* Where we divide a conception upon feveral principles, 
the whole number of the dividing members will be the produft 



LAWS OF THOUGHT. in 

divide without feeking for marks of difference, and 
as the enumeration of marks is the explanation of 
the nature of an objedl pofTeffing them, it is plain that 
no Divifion can take place without unfolding fome 
of the properties of the conception divided. It is 
true that trifling and ufelefs divifions, like thofe in the 
Sophifl of Plato (which perhaps were not intended 
to be regarded ferioufly) have brought the procefs 
into fome contempt ; but in many fciences a natural 
divifion, or one which is bafed upon natural proper- 
ties, and not upon fancies or trifling refemblances, is 
of great ufe both in arrangement and in fecuring a 
full and complete knowledge of a fubje£h Thus in 
that branch of medicine called Materia Medica, 
where the mode of treatment is purely divifive, it 
will be found that almoft all the various fchemes by 



of the numbers under the feveral principles multiplied toge- 
ther. In the example in the text, the principle of locality 
gives 5 fpecies, religion 4, and behaviour 2 5 then the whole 
number will be 5 X4X21Z40. For Europeans may be fubdi- 
vided into 4 claries according to their religion, and fo may each 
of the reft 5 then each of the fubdivifions may be again divided 
according to uprightnefs of conduct 5 fo that we have European- 
Jews who are juft — Afiatic-Jews who are juft, and fo on, up 
to 40 combinations. This logical fubtlety is of little practical 
importance, becaufe, amongft other reafons, many of the fub- 
divifions will commonly be entirely vacant. See Drobifch. 
Logik, § 119. 



ii2 OUTLINE OF THE 

which drugs are claffified, involve fo many diftinft 
theories of medicine. 

But as we defcend from a high genus to a fpecies, 
we mud: avoid a fudden leap over any of the fubaltern 
genera in the feries (divijio non faciat faltum), be- 
caufe their diftinftive properties may be overlooked 
at the fame time ; and hence divifion was defcribed 
above as the enumeration of the fpecies of the proxi- 
mate genus. Subdivifion is the procefs of dividing 
fome fpecies of a genus already fubjefted to that ope- 
ration ; and it may be repeated until we reach the 
loweft fpecies, which we cannot properly divide, 
though the individuals contained under it may be enu- 
merated. A divifion where the fpecies are not co- 
ordinate, although corredt in other refpe&s, would 
offer a bad arrangement for purpofes of fcience ; thus, 
Sciences fhould not be divided by a reader of Ariftotle 
into " Theoretical and Practical, together with Po- 
etry, Rhetoric, and Dialectic," becaufe the two firft 
are divifions, and the three laft are fubdivifions of a 
genus that has been omitted, namely, the Poetic 
Sciences. 

Logicians teft every divifion by the poffibility of 
reducing the conftituents to two, a pofitive and a 
privative conception. If A is a genus divifible into 
the fpecies x y and z, we may reprefent the dividing 
members as x and not-x, the latter being really equi- 



LAWS OF THOUGHT. 113 

valent to y and z. This divifion into two members 
(divifio debet effe bimembris) called dichotomy (5i%o- 
TOftLu) is alone purely logical, becaufe we know a 
priori^ and without any refearches into the particular 
cafe, that it muft be complete. But on the other 
hand it is comparatively ufelefs,* becaufe, of one of 
our conftituents, and that the larger, we know no- 
thing but that it wants the marks of the other. 
" Infincerity," fo long as it remains in our mind as 
a merely privative conception, implies nothing, ex- 
cept that it has not the mark or marks that fincerity 
has. The mind, however, does not allow concep- 
tions to retain their merely privative character ; fuch 
words as infinite, intolerant, undying, become fub- 
ftantial conceptions, as much fo as thofe with which 
they are contrafted by the form of their exprefHon. 

§ 58. Partition. 

The feparation of the parts of any individual ob- 
ject, as of a fword into blade and hilt, is termed par- 
tition. An individual (dro^ov) is that which cannot 



* Compare the mode of flaring this objection in Plato, Po- 
liticals, 262, C. D. roiovte ofov . . . tqov o-xicrQivrav. If, as Raffb^w 
and IVaitz fuppofe, Arijlotle had Plato in his mind in cenfuring 
the divifive method, as ufelefs in the difcovery of truth, (fee 
An. Poll. II. ch. 5, and An. Pri. I. ch. 31,) we believe that 
Plato faw its defects perfectly. 

I 



ii4 OUTLINE OF THE 

be divided without ceafing to be what it is ; its parts 
cannot have the name of the whole. When a genus 
is divided, every part of it . remains unchanged, and 
may have the name of the genus. The trunk and 
limbs of a man cannot be feverally called the man ; 
but a European is a man, and an Afiatic and an 
American. 

§ 59. Definition of a Conception. 

As Divifion afcertains the various claffes of ob- 
jects united under one Conception, fo does Definition 
afcertain thofe common marks which all the objefts 
poffefs, or that common nature reprefented by the 
conception. Divifion therefore anfwers to Gene- 
ralization (§ 49. ), and Definition to Abftra£tion; the 
former viewing the conception only as a clafs, the 
latter only as an abftraft nature or fet of properties. 
The attributes of this nature may none of them be 
peculiar to it when taken fingly, provided that the 
whole of them do not concur in any other concep- 
tion. Hence every definition will recount the marks 
of the genera above the conception it has to unfold, 
together with fome other mark called the Difference, 
by which this fpecies is diftinguifhed from every 
other. But this difference may only be a diftinftive 
mark when brought into its prefent connexion; apart 
from which it may be an attribute of fome high and 
wide genus. 



LAWS OF THOUGHT. 115 

As Definition and Divifion are but two fides from 
which the fame conception is viewed, they might be 
expected to lend each other afliftance. (§ 53.) In 
dividing fucceffively a fet of cognate conceptions, 
from the high eft to the loweft, we do in h£t bring in 
one by one the marks that compofe the definition, 
and hence the fulleft and moft complete definition 
would be formed after fuch a procefs of divifion had 
been gone through, provided of courfe that effential 
marks, and not mere accidental ones, had been brought 
in to divide by. Definition in turn, by enumerating 
the effential marks of a conception, furnifhes a guide 
to its genus, and its co-ordinate fpecies ; thus if 
" animal" were defined "an organized being with 
life and fenfation," its proximate genus would appear 
to be that of " organized living beings," divifible into 
thofe which had and thofe which were deftitute of, 
fenfation. 

The rules of Definition may be ftated here, as a 
help to underftanding the procefs itfelf, although they 
belong more properly to applied Logic : 

1. A definition muft recount the effential attributes 
of the thing defined (Definitio fiat per notas rei ef- 
fentiales). Thus in defining "words" as "the arti- 
culate figns of thoughts" we are not to introduce 
fuch a fuperfluous mark as " Words are the articulate 
figns by which an orator expreffes his thoughts," for 



n6 OUTLINE OF THE 

whilft this is true, it is not neceflarily found in the 
conception in our mind, and confequently has no 
place in the aft of analyfing it. 

2. The definition muft not contain the name of 
the thing defined; as this is precifely the word we are 
bound to explain. Thus if "life" is defined to be 
" the fum of the vital functions" we have not logically 
defined " life," as the word " vital," which implies 
life, ftands unexplained in the definition. This fault 
is called circulus in definiendo^ (alfo ^id.KKy\XQg rpovrog) 
becaufe vital is given to explain life, and life would 
be ufed probably to explain vital, fo that we mould 
travel "in a circle" back to our old difficulty. 

3. A definition muft be precifely adequate to the 
fpecies defined; (Definitio fit adaquata^ neque latior 
neque angujlior fuo definito). If it explains a fpecies 
below, it is faid to be too narrow, as when triangle 
is defined " a redlilinear figure with three equal fides 
and angles." If it is applicable to the genus above, it 
is too wide, as when we define words as cc the figns 
of thoughts," whereas there are other figns alfo. 

4. A definition muft not be exprefled in obfcure 
or figurative or ambiguous language. O ken's defi- 
nition of Philofophy cannot avail much ; it is " the 
recognition of mathematical ideas as conftituting the 
world." The Divine Nature has been reprefented 
as u a circle whofe centre is everywhere, and whofe 



LAWS OF THOUGHT. n 7 

circumference is nowhere ;" but this bold figure can- 
not for a moment be accounted' a definition. 

5. A definition muft not be negative, where it 
can be affirmative. " Evil is that which is not 
good. A point is that which has no parts and no 
magnitude. " Thefe definitions are to be judged ac- 
cording to our view of the poffibility of finding others 
of the affirmative form. Some conceptions are in 
their nature negative, as indivifibility, blindnefs, and 
.muft be defined negatively. 

The pofition which Definition holds in the con- 
ftraction of a fcience need not be difcufied here \ it 
belongs to the application of Logic. 

§60. Third power of Conceptions. Denomination. 

A Conception is not complete until it has received 
a name, to preferve and reprefent it for the future 
(p. 42). The principal divifions of nouns or names 
are the following. 

a. Nouns are either Proper, Singular, or Com- 
mon. A proper name reprefents a fingle object, 
apart from that connexion with others, which is ef- 
fected in abftraction (p. 98), as Socrates, Rome, 
Sirius. A common noun applies to a clafs of ob- 
jects, and their common marks or attributes, afcer- 
tained by abftraction, as man, city, ftar ; and it ap- 
plies to each and every one of the objects in that 



u8 OUTLINE OF THE 

clafs. A fingular noun applies to only one object, 
like a proper name, but then it is only fingular in its 
prefent application, as, a fong, this world, my horfe, 
the King of Pruffia ; it is evident that fong, world, 
horfe, king, are common nouns, and their fingular 
meaning is obtained by adding fome word of limita- 
tion. 

b. Diftributive and Collective Nouns are to be 
diftinguifhed. The former are common nouns, the 
latter nouns of multitude ; the former are applicable 
to each and every one of the objects they denote, 
the latter, though denoting many obje&s, can only 
be applied to them when combined, as army, fenate. 
Sometimes it is important to diftinguifh between the 
diftributive and collective ufes of words that may af- 
fume either form ; thus " All that glitters is not 
gold," means " all taken together," not " each and 
every thing ;" and " the Greeks conquered the Per- 
fians" means " the Greeks as a body," whereas " the 
Greeks loved philofophy" means " each Greek." 

e. Nouns are either Subftantives, Attributives, or 
Relatives. Subftantives are names of things, which 
have either in faft or in thought an independent ex- 
iftence, as Charlemagne, botanift, wifdom. Attribu- 
tives are nouns which affign a mark to a fubftantive, 
as great, good, docile. Relatives are pairs of nouns 
each of which implies the exiftence of the other, as 



LAWS OF THOUGHT. u 9 

father and fon, debtor and creditor, king and fub- 
jedts. The properties of relative conceptions muft 
be further explained below. 

d. Nouns are either Pofitive, which ftand for cer- 
tain definite marks and an afcertainable clafs of ob- 
jects, or Privative, which only imply the abfence of 
certain marks, and confequently belong to a vague 
and indeterminate clafs. Of the former, mortal, 
fincere, honeft, are examples ; of the latter, immor- 
tal, infincere, difhoneft. This is a diftin&ion of 
fome importance in Logic, as will appear hereafter. 

e. Nouns are either Univocal, Equivocal, or Anal- 
ogous, in their fignification. Univocal nouns have 
one meaning only, in which they are applicable to 
the objedts they ftand for. Equivocal have feveral 
meanings, and are in fa£t feveral words, with a cafual 
refemblance in form, as gall, for a wound and a bitter 
fubftance ; ball, for a dance and an orb ; light, for 
the contrary of darknefs and that of heavy. In 
analogous nouns, one meaning is extended to new 
fets of objedts from fome proportion or refemblance 
between them, as foot, extended from a part of an 
animal to the loweft part of a tree, a mountain, and 
the like. Where equivocal or analogous words are 
to be employed in Logic, it is requifite to give them 
the power of univocals, by adding words to fpecify 
the exadt application we mean to make of them. 



120 OUTLINE OF THE 

Analogous words pafs into equivocals, as foon as we 
lofe fight of the analogy that connects them ; this 
has occurred in poft, and in file as applied to a fixing 
of papers and a line of foldiers. 

§ 6 1. Privative Conceptions. 

It has been already obferved that befides concep- 
tions which arife from marks, there are others formed 
from the privation or abfence of marks. Our notion 
of kindnefs arifes from fome properties which a kind 
perfon always exhibits ; but whence our notion of its 
oppofite, unkindnefs ? From the want of the marks, 
whatever they may be, of kindnefs. So, too, in 
marking by a name any clafs of objects, as animal or 
ftone, we necefiarily imply that there are correfpond- 
ing clafies which are not animals and not ftones ; 
about which, it is true, we know very little, as we 
can only fay what they are not. Any pair of con- 
ceptions, a pofitive and a privative, muft, fpeaking 
abfolutely, divide the whole univerfe. Either in man 
or in not-man, all objects muft be found, — ftar, 
flower, form of government, moral quality, and any 
other things the moft unlike. But practically we 
limit this abfolute divifion ; though unkind does in- 
clude everything except the beings that {how kind- 
nefs, it would be abfurd to apply it to the whole of 
thefe. It is more convenient to think of fuch a pair 



LAWS OF THOUGHT. 121 

of conceptions as kind and unkind, as dividing be- 
tween them, not the whole univerfe, but fome proxi- 
mate genus, fay man or moral being ; fo that we mean 
to include in our notion cf unkind not every thing 
that is unkind, but every man that is fo. Such a 
larger conception, which a pofitive and a privatiye 
divide between them, may be called the fecond fphere 
of the pofitive.* 

Privative conceptions not only afford the means of 
varying the forms of thinking, by furnifhing for every 
affirmative judgment, equivalent negatives, and for 
every negative, affirmatives, but they enter into and 
affift the higher proceffes of the reafon in all that it 
can know of the abfolute and the infinite. To attri- 
bute the properties of one or many individuals to 
every other of the fame clafs is within the reach of 
the mere underftanding, and the brute creation enjoy 
fome mare of it \ but from the feen to realize an un- 
feen world, not by extending to the latter the pro- 
perties of the former, but by affigning it attributes 
entirely oppofite, is a prerogative of reafon alone. 



* The tevTEpa, oha-ia of Ariftotle (Cat. Ch. v.) may juftify the 
term fecond fphere. ProferTor De Morgan propofes to call it 
the unmerfe of the pofitive conception. The privative has 
been called by fome the contradi6tory ? by others the contrary, 
of the pofitive ; but either expreflion tends to confound con- 
ceptions with judgments. 



122 OUTLINE OF THE 

§ 62. Relative Conceptions. 

There is a clafs of conceptions which have the 
peculiarity that none of them can even be thought of 
alone, that the exiftence of each implies and depends 
on fome other ; thus a father implies offspring^ a king 
implies fubjeSfs^ a debtor a creditor ^ and fo on. Some 
of thefe are of diftinft things or beings, like the ex- 
amples juft given ; and are exprefled by nouns fub- 
ftantive ; but other relatives are only attributes, ex- 
prefled by adje£Hves ; thus larger implies /<?/}, akin 
implies a relationfhip to fome one, near^ high^ heavy , 
have reference to fome ftandard of diftance, ftature, 
or weight. 

A Relation is either fimple or complex ; Ample 
where it fubfifts between two correlates, as between 
debtor and creditor, complex where it is a relation of 
relations^ i. e. where it binds two or more pairs of re- 
latives together. Thus the word family implies not 
merely a fet of fimple relationfhips, between father and 
fon, brothers and fitters, but the adtion of thefe rela- 
tionfliips upon each other. The word Jlate in like 
manner implies not only the aggregate of the relations 
between the feveral clafles, but the mode in which 
thefe fimple 'relations aft on and modify one another. 

The relative conceptions that appear as adje&ives, 
as greats dijtant^ require no feparate treatment. Con- 



LAWS OF THOUGHT. 123 

ceptions have two kinds of marks, namely attributes, 
which belong to the conception in itfelf, and relations, 
which belong to it when viewed in connexion with 
other conceptions. To fay that man is mortal is an 
a£i of attribution, for mortality is a quality refiding in 
himfelf, without any reference to other beings ; to 
fay that man is long-lived is to bring him into relation 
or comparifon with other creatures whofe days are 
fliorter than his own. Relative adjectives then ex- 
prefs a particular kind of marks of conceptions. 

Simple relations exprefTed by fubftantives, are not 
more difficult to difpofe of. Thefe relatives always 
appear in pairs, — father and fon, ruler and fubjecft ; 
and that which is the more prominent in thought at 
a given time is called the relative, and the other its 
correlative. This order however can always be in- 
verted ; if it is the property of a ruler that he has a 
fubje6t, then inverfely he is a fubje£r, that has a ruler. 
But what is it that thus connects them ? A certain 
fait or ftate of facts, called the ground of relation, 
(fundamentum relationis); for relatio non eft ens per fe 
reale^fed per fuum fundament urn. In one of our ex- 
amples the ground of relation would be procreation of 
offspring, in the other, civil government. Now if a 
pair of relatives, with the ground of their relation, are 
to be refolved into fubftance and attribute, as other 
conceptions are, this will be poffible in three different 



124 OUTLINE OF THE 

ways, the fa&s of courfe remaining the fame, and the 
order of thought alone varying. The relative may 
be viewed as fubftance, and the correlative may be- 
come its attribute, or this may be inverted ; or thirdly, 
the ground of relation may become the fubftance of 
which both the correlatives are attributes ; thus, we 
attribute to the ruler, that he has fubjefts, or to the 
fubjedts that they muft have a ruler, or to civil go- 
vernment that it implies a ruler and fubje&s. Nor 
is it neceffary to break the fymmetry of the do<?crine 
of conceptions in order to find a place for what may 
at firft appear to demand it by their peculiarity of 
form. 

§ 63. Abjlracl and Concrete Reprefentations. 

Abftraft and concrete are relative terms ; when 
a higher conception is feen to exift in a lower, or in 
an intuition, as we fee the marks of animal in the 
conception horfe or a horfe, we are faid to fee the 
abftraft in the concrete. So of two cognate con- 
ceptions, the more abftra£t bears the name of the 
abjiracl^ the more fully determined we call the con- 
crete. 

The received explanation among logicians in this 
country is that an abftraft term is the name of a 
quality confidered apart from the fubjeft in which 
we fhould look to find it, as prudence, ftrength \ and 



LAWS OF THOUGHT. 125 

that a concrete term is a name expreffing the quality 
as refiding in fome fubjeft, as prudent, ftrong. There 
is an analogy between this narrow fenfe, and that 
affigned by us ; we fay that the abftraft is to the 
concrete as univerfal to particular, and they, that it 
is as the general quality to particular cafes of it. # 

§ 64.. On the nature of general Notions. 

There is a pretty general agreement at prefent as 
to the mode of the exijlence of general notions ; the 
differences of opinion referring chiefly to the ufe that 
fhall be made of them. Formed in the mind, they 
are not entirely dependent upon its mere arbitrary 
decifion ; becaufe in moft cafes there are properties 
in the objects around us which compel us to gene- 
ralize in a particular way. Every nation, for ex- 
ample, would without any exprefs convention put 
men into one clafs and horfes into another, becaufe 
the common properties of men are fo marked and 
ftriking, that they feem as it were to cry aloud to be 
claffed together. No one would be abfurd enough 
to negledt fuch fimilarities ; and to put fome men 
and fome horfes invariably into one clafs, becaufe 



* See the excellent note in Trendelenburg. Excerpta : on 
§ 36. Alfo Waitz on Organon. Comm. on 8 1. 6. 3. Tren- 
delenburg on Ar. de Anima, 478. 



126 OUTLINE OF THE 

they were white, and fome other men and fome other 
horfes into one clafs becaufe they were black ! Ge- 
neral notions exift in the mind alone ; but they are 
founded on common properties which exift without 
the mind, not in a feparate ftate, but as inherent in 
the obje£ts of intuition. Further, thefe common 
properties were given to the various objefts by de- 
fign. For example, when the fame vertebral column 
is found in a hundred fpecies of animals, fometimes 
joined to large and powerful limbs, fometimes to 
fmall, rudimental ones, now to wings, now to fins, 
and now to arms, fometimes carried vertically, fome- 
times horizontally; and when, amidft all the fpecific 
variations, many of them modifying its own ftruc- 
ture, the vertebral column is eafily recognized as 
fundamentally unchanged, it is natural to infer that 
the pofleffion of this part of the frame was pre- 
ordained to be the link of connexion of thefe fpecies, 
and that in forming a clafs of "Vertebrate Animals" 
we are feeking after a form or idea which was in the 
Divine Mind when animals were created. So that 
general notions exift without the mind of man, in as 
far as they are in another mind. The Divine Mind 
ftamps them on material things ; the human reads 
them there. 

With the controverfies upon this queftion, and 
with the various opinions indicated by the names, 



LAWS OF THOUGHT. 127 

Realifm, Nominalifm, and Conceptualifm, we need 
not concern ourfelves much in this place ; they muft 
be ftudied hiftorically, in their connexion with The- 
ology and in the order of their development, before 
we can hope to underftand them. Still a few re- 
marks may be of ufe in guiding thofe who have time 
to purfue the ftudy. 

The queftion concerns Univerfals {univ erf alia), 
or thofe general properties which many things (hare 
alike, and which are acquired by the mind only by 
abftracting from the things that exhibit them (§ 49). 
Thefe Univerfals have names of their own, juft as 
much as the moft tangible things ; whitenefs, huma- 
nity, animal, may ferve as examples. Now the quef- 
tion, broadly ftated, to the neglecT: of many nice 
fubtleties and fhades of opinion brought out in the 
hiftory of the controverfy, is this — Are thefe Uni- 
verfals real exiftences, apart from the mind that has 
formed them by abftraction, and independently of 
the things in which alone they appear to us, — or are 
they mere modes of intellectual reprefentation, that 
have no real exiftence, except in our thoughts ? 
Thofe who adopted the former alternative were called 
Realifts y thofe who adhered to the latter might fitly 
be defignated by a name of later origin, as Con- 
ceptualifts, if we mould objecT: to the name of Mo- 
derate Nominalifts, which indeed would imply that 



128 OUTLINE OF THE 

they held thefe Univerfals to be mere names. To 
each of thefe more moderate opinions belongs a cog- 
nate exaggeration ; fo that there are four principal 
anfwers to the queftion — what are Univerfals. 

I. That of the Ultra-realifts. Univerfals, or the 
Ideas of things, are real exiftences, nay, inafmuch as 
vifible things change, grow, decay, and perifh, the 
Univerfals or Ideas are the only real exiftences, for 
they are fubjedt to none of thefe conditions. Wife 
men perifh \ but the idea of wifdom, of which they 
partake, after which they have their name, perifhes 
not, does not change, — is the fame in the Seven 
Sages as in the philofophers now living. In conformity 
to thefe ideas the world was created ; and thus they 
even governed and guided the creating mind itfelf. 
This form of Realifm has been attributed to Plato ; 
but it is probable that he flopped fhort of believing 
that the Divine Mind was fubjeft to the ideas. What 
general notions are to our minds — he probably held 
— ideas are to the fupreme reafon (vou$ fiocaiteug) ; 
they are the eternal thoughts of the divine Intellect, 
and we attain truth when our thoughts conform with 
His — when our general notions are in conformity 
with the ideas. It is however very remarkable that 
Plato has left his opinions upon this important point 
open to a reafonable doubt.* 

* Stalbaum, Prol. to Plat. Farm. p. 269. 



LAWS OF THOUGHT. 129 

2. That of the Realifts. Univerfals exift inde- 
pendent of things and of our conceptions of them, in 
the Divine Intelle6t. Under various forms this doc- 
trine — of univerfalia ante rem — was the docTxine of 
the Schools before Rofcelin, and of the Realift School- 
men after him. 

3. That of the Moderate Nominalifts. Uni- 
verfals exift as a produit of the mind only \ they are 
formal reprefentations of things, conftru6ted by the 
mind through the afliftance of language. Occham 
founded his Nominalifm (fo called) upon the pofition 
Nullum univerfale ejl aliqua fubjiantia extra animum 
exiftens.* Many fhades of opinion, however, are to 
be detected among the Moderate Nominalifts ; and 
that of the Conceptualifts, reprefented by Abelard, 
fhould be particularly ftudied. 

4. That of the Ultra-Nominalifts. Univerfals are 
mere names ; and the only realities are individual 
things, which we group together by the aid of names 
alone. The name of Rofcelin is ufually connected 
with this opinion; but in what fenfe he held that 
Univerfals were only flatus vocis^ we cannot decide 
from the fcanty and adverfe accounts in our pof- 
feflion. 

Before we indicate fome of the principal fources 

* Logic a, 1. 15. 
K 



130 OUTLINE OF THE 

of the hiftory of Nominalifm and Realifm,one remark 
is to be made, which, if it will not remove the diffi- 
culties of the fubjeft, will perhaps define the common 
ground upon which the more moderate of both the 
adverfe parties may be brought together. Making 
allowance for much confufion of ftatement in the 
fcholaftic writers, and for extreme afTertions, which, 
there is reafon to think, their authors underftood in 
a modified fenfe, we have two views of the nature of 
general notions ; that of the Realift, who maintained 
that they exift in the mind and alfo without it — in 
the Divine Mind ; and that of the moderate Nomi- 
nalift, who held that they exift only in the mind as 
notions, and that we ufe names to fix and recall 
them. Now I venture to think that the interminable 
conteft between Platonift and Ariftotelian, Realift 
and Nominalift, is, at bottom, not fo much a quef- 
tion of what univerfals are, as of how they mall be 
treated ; not fo much a queftion of Metaphyfics, as 
of Method. Upon the nature of general notions 
there is a large amount of agreement between the 
parties : the Realift believes, with the Nominalift, 
that they are in the human mind, whilft, if the No- 
minalift believes at all that the world was created by 
defign, he can fcarcely efcape from recognizing the 
Realift's pofition, that fuch ideas as animal, right, mo- 
tion, muft have had their exiftence from the begin- 



LAWS OF THOUGHT. 131 

ning in the creative mind. Whence then the con- 
troverfy ? The burden of Ariftotle's objections to 
the Platonic fcheme of ideas is, that it teaches what 
cannot be known, and gives out as certain truth 
what lies far beyond the reach of our powers of in- 
veftigation. " Inftead of being content," he would 
fay to the Platonift, " with clarifying particular ob- 
jects fo as to form general notions, which we could 
always compare with the objects, as being infeparable 
from them, you jump to certain ideas, feparate from 
the objects, though they caufe and determine the 
manner of their exiftence, fixed whilft thefe are 
changeable, eternal whilft thefe pafs away. Be it fo ; 
you offer thefe tranfcendent ideas to our understand- 
ing — you muft remove the difficulties which the un- 
derftanding meets in receiving them. How do you 
know that they exift ? For we muft not, in order 
to explain the world which we fee, devife another 
world, of ideas, which no eye has feen.* Again, 
how are they connected with the things to which they 
belong ? The man, for inftance, with the idea of 
humanity ? to fay that things c participate' in, or c are 
copies' of, the ideas, is to avoid the difficulty by 
vague metaphorical language. Muft there be an idea 



* So Occham — " Entia nonfunt multiplic anda prater necef- 
Jitaiem" 



132 OUTLINE OF THE 

for every fenfible obje£t ? If fo, before Socrates 
could be born, there muft have been an eternal idea 
of Socrates ; which would lead us to a multiplication 
of ideas too great even for the imagination. In a 
word, you cannot explain the properties of thefe ideas 
without vaguenefs and felf-contradi£tion ; and there- 
fore, fhould not affume them to exift and found a 
fyftem upon them."* 

If this view be correct, Ariftotle does not fo much 
intend to deny the exiftence of ideas, as to maintain 
that the evidence for them is inefficient, and that no 
fyftem can ftand fecure upon fo weak a foundation. 
And looking to the paradoxical and feemingly incon- 
fiftent ftatements of Plato on the one handf and the 



* Compare, Metaphyf. XIII. (M). 4, p. 1078, b. Ed. Berol. 
Ibid. 5, p. 1079, b. 36. Ibid. I. (A) 6, p. 987. Ibid. 9, p. 
990, b. Ravaifon, Metaphyfique d'Ariftote, III. ii. 2. Re- 
nouvier, Hiftoire, II. p. 42. To avoid mifunderftanding, let 
me remark that the refemblance between Ariftotle and the No- 
minalift lies only in his denying zfeparate exiftence to univer- 
fals. " Different philofophers have maintained that Ariftotle 
was a Realift, a Conceptualift, and a Nominalift, in the ftricleft 
fenfe." Sir W. Hamilton. 

f For he fpeaks of the ideas, now as if they were merely 
mental conceptions, now as independent exiftences. StalbaunCs 
Parm. Prol. p. 273. And he does not clearly explain where 
the ideas exift, and whether they depend on the Divine Mind, 
or It upon them. Ibid. p. 272. 



LAWS OF THOUGHT. 133 

evident mifapprehenfions of Ariftotle upon the other, 
I can conceive it poffible that a fage mediation might 
have reconciled thefe two great fpirits ; and Ariftotle 
might have owned that the univerfal notions in his 
mind might anfwer to certain ideas in the Divine, 
whilft his illuftrious mafter might have confefTed that, 
putting revelation out of the queftion, there is no 
way to the abfolute — to knowledge of the ideas — 
except a careful obfervation of and reafoning from 
the fa&s we poflefs, in our own mind and in the world 
around us. Plato indeed was an inductive reafoner, 
not inferior to Bacon himfelf \ though the one con- 
fined himfelf too exclufively to the fa£ts of the human 
mind, and the other to thofe of the external world. 
The queftion then between Plato and Ariftotle, as 
any one may fatisfy himfelf who will refer to the 
original places in the works of the latter, chiefly 
concerned Method, and did not turn fo much upon 
a belief in the exiftence of ideas as upon the right to 
aflume them as the ground of teaching. 

It is impoffible here to follow out this hint through 
the fcholaftic controverfies, where the nature of uni- 
verfals was difcuffed in connexion with religion, as it 
had been in its bearings on fcience; but its importance 
will be felt in that region alfo. We muft diftinguifti 
between the opinions, that univerfals cannot poffibly 
exift, and that the attempt to explain them as inde- 



i 3 4 OUTLINE OF THE 

pendent natures involves us in logical difficulties and 
contradictions. 

Thus diverted of one element of confufion, the 
queftion will affume a lefs repulfive form \ but its 
difficulties do not difappear, nor is its importance 
lefTened. Indeed at the prefent day the great divifion 
between fcientific men has affumed this form. " We 
cannot attain truth," fay the more bigoted followers 
of Bacon, " except by confining ourfelves fimply to 
the fa£ts of nature, and their arrangement. We muft 
not view them in any theological connexion ; we 
muft not call in any metaphyfical idea to affift us in 
grouping them. We have fimply to arrange them, 
ufing names and language for that purpofe." Here 
again the queftion is regarded as pertaining to method; 
in other words the exiftence of the Deity, the exift- 
ence and nature of Ideas, are not denied, they are 
only declined or put afide, whilft it is denied ftrenu- 
oufly that they can be brought in to aid man in the 
inveftigation of truth. The opinions of fuch writers 
as Augufte Comte are but the lateft exhibition of 
pure Nominalifm, under its logical as oppofed to its 
metaphyfical form. " We muft regard individual 
things as the only realities for us^ and language as the 
means of difcoveringand preferving their connexion."* 

* Upon the hiftory of Nominalifm and Realifm may be con- 
fulted — Brucker, vols. iii. and vi. Tennemann's Manual. The 



LAWS OF THOUGHT. 135 

§ 65. ^ueftions about Conceptions* 

When a conception is recalled to the mind, under 
what form does it appear ? Under that of a bare 
word, or of all the marks which we abftra£ted to form 
it, or of fome fingle object ufed as the reprefentative 
of all the others of the fame clafs ? We have feen 
already (§25) that the word, or the array of marks 
may be employed to recall the conception. In any 
propofition which conveys a definition, we have 
examples of both forms. In fuch a fentence as 
cc honefty is uprightnefs in all dealings w 7 hich refpedr, 
property," the former of the two conceptions is ufed 
as a counter (notionis tejjera) to reprefent the marks, 
which the latter explicitly conveys ; in the phrafeo- 
logy adopted above, " honefty" is a fymbolical, and 
" uprightnefs in dealings which refpecl: property" a 
notative conception. As to the third opinion, the 
underftanding, which for convenience 5 fake puts fym- 
bols for true conceptions, does on the fame account 

brilliant Preface by Coujin to " Ouvrages inedits d'Abelard." 
Paris, 1836. Alfo Coujin, Lemons. 1829, Leg. 9. Haureau, 
Philofophie Scolaftique, 1850. Hegel, Gefchichte, iii. 180. In 
Degerando, Hiftoire, i. p. 235, there is a good account of the 
(hades of opinion in the two parties. Sir W. Hamilton's Reid, 
p. 405. Dugald Stewart, Phil, of Human Mind, vol. i. ch. 
4. § 2. Brown's Lectures. Biihop Hampden's Bampton Lec- 
tures : Lecture ii. and Notes. 



136 OUTLINE OF THE 

put examples of a conception inftead of the concep- 
tion itfelf, the fingular inftead of the general. For 
the notion animal, I think of a particular horfe or 
cow ; for honefty, of fome honeft man ; for juftice, 
of fome Brutus or Ariftides ; for city, of London or 
Paris ; but always with a confcious refervation that 
there are many points about this particular cafe which 
are not general, and do not belong to the conception. 
But it will hardly be queftioned by any, that the un- 
derstanding can, by a fomewhat feverer felf-controul, 
throw afide the particular cafe, and retain only the 
common marks which belong to the whole concep- 
tion. For we muft admit the power of abstracting 
fome marks from the reft, as the having life^ which is 
the mark of animal^ is abftra£ted from the thoufand 
different circumftances of fize, fhape, colour, food, 
temper, which diftinguifh animals from each other; 
elfe how are conceptions formed ? And if we can 
abftra£t the marks from the accidents, furely we can 
retain them in our grafp when abftra£ted. 

ii. Are reprefentations of the imagination — the no- 
tion we have of a landfcape from fome poetical de- 
fcription, for example — to be confidered as intuitions 
or conceptions ? If the defcription could be fo com- 
plete, and the reader's apprehenfion fo accurate, that 
every portion of the landfcape were diftin£tly feen, 
and we could diftinguifh that fcene from every other, 



LAWS OF THOUGHT. 137 

even from one that refembled it mod: clofely, then it 
would be in accordance with the definition we have 
given (§ 48) to call it an intuition. But this, I fup- 
pofe, is never the cafe. The poet can defcribe a lake- 
fcene with diftinftnefs enough to prevent our having 
an impreffion from it of any other kind of landfcape, 
as a plain with a diftant city, or the cliffs of the fea- 
ftiore. But ftill the defcription muft be far too ob- 
fcure to prevent our miftaking this lake-fcene for 
one clofely refembling it, or even our recalling fome 
lake we remember, to fupply the deficiencies of his 
delineation, although we know that we are adopting 
one fcene, whilft he drew another. He can limit 
our general notion of landfcape to fome particular 
fpecies, but not to this individual landfcape — can re- 
duce our "all" to "fome," but not to "this." 
Therefore, fuch an image is a conception, ufed par- 
ticularly^ i. e. only fome part of it is called up. It 
is a reprefentation of fome landfcapes, but not of one^ 
to the exclufion of the poffibility of confounding it 
with others. 

iii. Can there be abftraftion without generaliza- 
tion, as Archbifhop Whately maintains ? " Suppofe 
we are fpeaking of the King of France," fays he; "he 
muft actually be either at Paris or elfewhere; fitting, 
ftanding, or in fome other pofture ; and in fuch and 
fuch a drefs, &c. Yet many of thefe circumftances 



138 OUTLINE OF THE 

(which are feparable accidents, and confequently) 
which are regarded as non-ejfentlal to the individual, 
are quite difregarded by us ; and we abftraft from 
them what we confider as eflential ; thus forming 
an ab/lraSf notion of the Individual. Yet there is 
here no generalization." A great error lies hid in 
this pafTage — that of not perceiving that the power 
of feparating circumftances called eflential to the in- 
dividual from thofe which are not fo, refults from 
former generalizations. How do we know that 
cc fitting" or "ftanding" is not eflential to a king? 
How do we know that a crown and a robe of ftate 
are feparable from the King of France ? By prior 
generalization ; by the help of the conception we 
have formed of a king already. If we had never 
known of other kings, or the fame king at other 
times, we fhould have looked on the accidents and 
eflentials of the King of France as alike eflential. 
We know that "fitting" is not eflential, becaufe we 
know that kings fometimes do not fit. There is no 
abftradtion without generalization ; and in the cafe 
before us, we abftrait, to refer to a former general 
notion or conception. 

§ 66. Summary. 

The firft part of Logic explains that power of the 
mind which groups fingle objects into clafles, fo that 



LAWS OF THOUGHT. 139 

the claffes have names and attributes of their own. 
Its principles are thefe : 1. The nature of every 
higher notion is found in the lower ; confequently 
2. The name of the higher may always be applied to 
the lower. Thus man may be called an animal, be- 
caufe the marks of life and fenfation which diftinguifh 
animals are found in him. 3. The higher notion 
{genus) includes the lower notion (/pedes) with other 
fpecies, and is therefore of wider extenfion than it. 
But the fpecies implies more marks — has a fuller de- 
finition — than the genus ; and is faid, therefore, to be 
of deeper intenfion than it. 4. That fet of marks 
which diftinguifhes any fpecies from the other fpecies 
in the fame genus is called its Specific Difference. 
5. The whole nature of a fpecies is afcertained, and 
its definition given, when the properties of the genus 
and thofe which make the fpecific difference are 
brought together. 6. We afcend from lower con- 
ceptions to higher by throwing away fpecific dif- 
ferences, /. e. by abftraction. We defcend to lower 
ones by refuming the marks we have thrown away, 
i. e. by determination. 7. In a fyftem of fubordi- 
nate genera each muft contain the individuals in- 
cluded in the loweft. 8. Co-ordinate fpecies cannot 
contain the fame individuals. 9. The conception of 
an objecT: confifts of the aggregate of its marks, 
with the notion of exiftence fuperadded. 10. Sin- 



140 LAWS OF THOUGHT. 

gular obje£ts are invariably referred to and viewed 
through general conceptions, n. A conception is 
complete and adequate, when it can be refolved at 
pleafure into its implied marks by definition, and 
into its contained fpecies by divifion. 12. Two 
marks which ftand to each other as pofitive and pri- 
vative, like wife and unwife^ are called contradictory, 
becaufe it would be a contradiction in terms to aflign 
them at the fame time to the fame objeft. Two 
marks are called contrary, when it is known a pos- 
teriori by experience, and not a priori by the very 
form of expreffion, that they cannot belong to the 
fame object, as wife and wicked^ warm and frozen. 



OUTLINE OF THE LAWS 
OF THOUGHT. 

PART II. 
JUDGMENT. 

OvoEfxiciv yaq ours ouTcog our ifceivojg 7rpci%iv oufi' 
aTrpatilav dnXoT ra (puvnQevra, irpiv av rig ToTg ovo^ocai 
to, pyjfjLara Kip<x>jy\. 

Plato. 




JUDGMENT. 

§ 67. jfudgment Defined. 

'VERY aft of judgment is an at- 
tempt to reduce to unity two cogni- 
tions. When one decides that " So- 
crates is wife/' it is that hereafter one 
may, by combining the two notions, think of " the 
wife Socrates." Again, when one decides that " the 
world is not eternal," it is that hereafter one may re- 
frain from combining the two notions as " the eter- 
nal world." 

A Judgment then is an expreflion that two no- 
tions can or cannot be reconciled — that the marks 
of the one may or may not be henceforward affigned 
to the other.* A propofition is the expreflion of a 
judgment in words. 

* This definition is rejected by Mr. Mill, Logic, vol. i. 
p. 116, feq. on the ground that a judgment exprefles the 
agreement of things rather than of notions. But the notions 
are controlled by the things, otherwife affent and diffent would 
be arbitrary. I am forced to fay " the day is fine" when the 
iky is cloudlefs, becaufe my perceptions muft correfpond with 



144 OUTLINE OF THE 

Though the truth or falfehood of a judgment, 
and confequently its value, depend upon its corre&ly 
reprefenting things without us, rather than thoughts 
within us, it is primarily concerned with thofe repre- 
fentations in the mind by means of which alone 
things are brought into the arena of thought, whe- 
ther as fingle objects or as the gound of abftradt and 
general notions. 

Every judgment has three parts; the fubjeft, or 
notion about which the judgment is ; the predicate, 
or notion with which the fubjeft is compared; and 
the copula or nexus, which exprefles the mode of 
connexion between them. The fubje£t and predi- 
cate are called the terms of the judgment, i. e. the 
extremes or boundaries [termini) which it brings 
together. 

§ 68. Doffrine of Relation in yudgments. 

When we examine fuch a judgment as " Man is 

the fafts. This correfpondence then the definition in the 
text is confidered to imply ; and it is retained becaufe it is be- 
lieved to be the only one that includes and defcribes every 
kind of judgment. But the weight allowed to Mr. MilVs 
objection will depend on the theory of Perception we adopt, 
and that great metaphyfical queftion we cannot here difcufs. 
See however, Reid, Int. Powers, EfTay vi. 3. Hamilton's Reid. 
Appendix C. and D*. Coufm, Hiftoire de la Phil. Lecon 2^. 
Edinburgh Review, vol. Hi. Art. " Reid and Brown. " 



LAWS OF THOUGHT. 145 

a rational animal " (which, trite as it is, will ferve 
for our prefent purpofe) we find that the fubje£t and 
predicate are exa£Hy co-extenfive ; in other words, 
no obje£t comes into the clafs of rational animals 
which is not alfo in man, and converfely no obje& 
comes under man which is not alfo under rational 
animal. The two conceptions, the one fymbolical 
the other notative,* are derived from and reprefent 
the very fame clafs of beings. This equality of fub- 
je£t and predicate is an important property of the 
judgment, for it conveys the power to fubftitute the 
one conception for the other, at pleafure. 

Other judgments want this property. To fay that 
" trees are plants" is to fay indeed that no obje£t is 
a tree which is not alfo a plant ; but then there are 
plants which are not trees ; fo that plant and tree are 
not conceptions of equal extent. 

It is true that the copula — the " is" or " are" 
which couples the conceptions — does not exprefs 
the great difference we have noticed ; being ufed in 
common language for either relation of the two terms. 
But as the corre£tnefs of fome trains of reafoning de- 
pends entirely upon obferving the relation of coinci- 
dence between fubjeft and predicate, it is ufual to alter 
the copula in fome way, to exprefs it, as by faying " is 

* P. 45- 

L 



146 OUTLINE OF THE 

defined to be — is divided into — is co-extenfive with." 
In the prefent book, inftead of the copula " is" or 
" are," the mathematical fign of equality (=) will 
be employed in affirmative judgments in which the 
predicate is dijiributed^ or taken entire. 

Every affirmative judgment indeed may be re- 
garded as an equation of fubjeft and predicate, as 
every negative is a decifion that an equation cannot 
be eftabliftied. By " All men are mortal" I mean 
that all men are equal to fome mortal creatures \ and 
by "■ Some plants are poifonous " I mean that a part 
of my conception of plants coincides with a part of 
the conception of poifonous things.* 

§ 69. The Two Predicable-Clajfes. 

Logicians have always formed a clarification of 
predicates according to the relation in which they 
ftand to their refpe&ive fubjefts. We propofe to 
give the fimpleft form to this fcheme of Predica- 
ble-Clafles, or clafles of conceptions which can ftand 
as predicates, taking Ariftotle's dodtrine as the bafis. 

Every judgment, according to Ariftotle, declares 
either a genus, or the property, or the definition, 
or an accident f (ysvo? — i&ov — opog — <rv(jt.@E@wo$) of its 
fubjeft. 

* Sir William Hamilton, 

•j* Top, A. ch. iv. Of the names which A. adopts for the 



LAWS OF THOUGHT. 147 

The genus is that mark or attribute, which, 
whilft it never fails to accompany the fubjecl, be- 
longs to other fubjec~rs equally; as in "Envy is a 
paffion." The property is that mark or attribute 
which belongs to the fubjecT: invariably, and to no 
other, without being the mark that would be ufed 
if we had to explain the nature of the fubjecT: ; as 
" Man has the faculty of fpeech." Definition is the 
mark, or aggregate of marks, that would explain the 
very nature of the fubjecl: ; as " A ftate is a commu- 
nity governed by its own laws." Laftly, the acci- 
dent is an attribute that happens to attach to the fub- 
ject, but is feparable from it ; as " Life is fweet." 

The difference, or that mark or marks by which 
the fpecies is diftinguifhed from the reft of its genus, 
does not occupy a diftincl: pofition in Ariftotle's lift, 
but is faid to belong naturally to genus (cc$ olaav 
ymmv).* The fpecies may be regarded as compofed, 
not of the marks of the genus and the difference, fo 

claffes, yhog, and perhaps h'pog, feem to exprefs rather the exten- 
fion, the others the intenfion $ but he ufes them as having both 
powers. The common divifion of Predicable-claffes is that of 
Porphyry , into Genus, Difference, Species, Property, and Acci- 
dent. 

* Like the genus, the difference can be 'predicated of many 
things differing in fpecies. But the genus is predicated Iv r« 
ri la-ri, the difference h vw ttoTov tL Alex, Aphrod. in Berlin 
Ed. of Arift. Top B A. ch. iv. 



148 OUTLINE OF THE 

well as of thofe of two concurrent or communicant 
genera : for the difference is but a genus which from 
its overlapping part of another is ufed as a diftin£tive 
mark of that part which it overlaps. If (for an eafy 
example) in analyfing our notion of " the red-flower- 
ing currant" {Ribes fanguineum) we regard "currant" 
as the genus and u red-flowering" as the difference, 
we may alfo regard " red-flowering" as a wide genus, 
wider in fa£t than " currant," and therefore we may 
fay that our notion of the plant is formed from the 
concurrence of two genera.* 

This we fuppofe to be Ariftotle's meaning in con- 
sidering difference as having the nature of genus. 
But we are now to notice that he examines and ar- 
ranges his four Predicable claffes according to this 
teft — Can each of them, without logical fault, change 
places with its fubjeft. In other words, is each of 
them co-extenfive with its fubjeft or not ? The re- 
fults of the teft will be apparent from an account of 
each of the claffes. 

* Let A be the clafs of " red-flowering" things, B the clafs 
"currant ;" then x, the part of each which is in the other, will 
be our notion of " red-flowering currant." 







LAWS OF THOUGHT. 149 

Definition # is a defcription which manifefts com- 
pletely the nature of the thing defined. Such a de- 
fcription would of courfe enable us to identify the 
fubje£t, and to diftinguifh it from all other notions. 
And therefore it muft be applicable only to the fub- 
je£t, otherwife it manifefts, not the peculiar nature 
of the thing defined, but its common nature, the quali- 
ties which it fhares with other things. As being 
applicable to the fubjeft and to no other notion, it is 
co-extenfive with it, and therefore may change places 
with it in the judgment. It is juft as true to fay that 
u every rational animal is man" as that " every man 
is a rational animal." But if we faid that "man is 
a warm-blooded animal," or that "man is a civilized 
animal," neither of them would be a definition, nor 
could the predicate in either become the fubjeft, 
without fome limitation. The former is a defcrip- 
tion that applies to more than man, the latter to a 
part only of man ; and of courfe neither of them 
would enable us to apprehend exadtly what man's 
nature was. 

Property f is not eafily diftinguiftied from defini- 
tion. Indeed Ariftotle confeffes that property (i'hov) 
i. e. fomething peculiar to the fubjedt, and eflentially 



# Top. A. ch. v. More fully treated of in Top. Z.paJJim* 
f Top. A. ch s iv. and v e 



150 OUTLINE OF THE 

its own, is a name which would naturally include 
definition, and would mean fome attribute which 
belongs to all the fubjeft and to it only ; but he adds 
the fpecial limitation " without declaring the effence 
or nature of the fubjeft." Every quality then which 
belongs to all the fubje£t, and to no other, is a pro- 
perty, provided it be not ufed in the definition. It 
is co-extenfive with the fubjeit, and can therefore 
change places with it in the judgment without logical 
fault. Thus " Man is capable of learning to write 
and fpeak corre&ly" might become " Every being 
capable of learning to write and fpeak correftly is a 
man." 

But this fubtle metaphyfical diftin&ion between 
the definition and the property is as difficult to main- 
tain as it is unneceffary for the purpofes of pure logic. 
How can we rely on being able to feparate our notion 
of the nature or effence of a thing from the proper- 
ties which accompany that nature ? Let it be the 
definition of man that he is " a rational animal" and 
the property, that he is " capable of fpeaking cor- 
rectly ; " and how can we fay that the latter is not 
in the effence, yet neceffarily follows from the effence 
of man ? It is a part of the effence, for " rational" 
implies it. In like manner, all the properties feem 
to be implicitly contained in every perfect definition. 
No criterion can be given for diftinguifhing between 



LAWS OF THOUGHT. 151 

the. efTence and the infeparable accompaniment of the 
efTence ; and a larger acquaintance with the nature 
of things makes it evident that what one fcience re- 
gards as a property another muft confider as efTential, 
and that there is no one paramount quality which is 
abfolutely efTential and can never be degraded to the 
rank of a property. 

The predicable Genus is a clafs of which the fub- 
je<9: is a contained part. It declares, though not 
completely, the nature of the fubje£t. A fubje£r. 
may be included in many different genera by different 
fets of marks ; a man may be good, brave, rational, 
mortal, fallible, fick, learned, and fo on. But fome 
of thefe qualities, as wholly feparable from the nature 
of man, are to be confidered not as genera but as ac- 
cidents. Genus, as being of the very nature of the 
fubje£t, is infeparable from it. As including the fub- 
je£t in common with other fpecies, it is not co-exten- 
five with it. Hence the tranfpofition of the fubjeft 
and predicate in a judgment which predicates the 
genus, cannot take place ; " all rofes are plants" can- 
not become "all plants are rofes." 

Accident is a quality which belongs indeed to a 
fubje£t, but can be taken away from it without de- 
ftroying its nature or efTence. We predicate acci- 
dent when we fay that " a man is fpeaking." Acci- 
dent cannot change places with its fubjeft, becaufe it 



i 5 2 OUTLINE OF THE 

does not apply to the whole of that fubjeft and to it 
alone. But a criterion is wanting to diftinguifli be- 
tween accident and genus or fpecies. It is an acci- 
dent to the people of this country that they were 
born in it ; becaufe we might conceive them to have 
been born elfewhere ; but then it has modified their 
nature or efTence, and we understand by Englifhman 
not merely one who was born within the four feas, 
but a man of particular feelings, views, and privileges, 
which are parts of his very nature. Here accident 
and genus or property feem to become confufed. It 
is an accident too that this nail is rufty and that gui- 
nea bright, but then it fhows that the gold has a 
property — of refifting oxidation — which the iron 
wants, and might ferve to place them in two diftindt 
fpecies of metals. Ariftotle a£tually fpeaks of man 
as an accident of the genus animal, although it is 
commonly reprefented as one of its fpecies ; * no 
doubt becaufe we might conceive that fpecies anni- 
hilated without the deftru£tion of the genus. It does 
not appear then that the predicable accident can at 
all times be diftinguifhed from the others, which 
would be a valid objection againft retaining the doc- 
trine in which it holds a place. 

* Cat. vn. 14. In quoting the paflage Crackanthorp fays 
" Omnia inferiora accidentia funt refpe£hi fuorum fuperiorum." 
See too Cat. vn. 13. Pacius : marginal note. 



LAWS OF THOUGHT. 153 

We propofe to abandon, as at leaft unneceflary for 
logical purpofes, the diftinftion between property and 
definition, genus and accident ; and to form, as Arif- 
totle has alfo done, two clafles of predicables ; one of 
predicables taken diftributively, and capable of be- 
coming fubje&s in their refpe£Hve judgments with- 
out limitation, the other of fuch as have a different 
extenfion. In the former, the predicable has the 
fame obje£ts as its fubje£t, but different marks or a 
different way of reprefenting the marks. In the lat- 
ter there is a difference both in the marks and the 
objects. The former may be called Definition, or 
Subftitute ; the latter, Attribute. 5 * 

§ 70. Definition explained* 

Every predicate which denotes exa£Hy the fame 
clafs of things as the fubje6t, may be called a defini- 
tion. Whether it unfolds the genus and difference, 
or the property, or only fubftitutes one fymbolical 
conception for another, it is ufeful to mark out for us 
more clearly the limits of the fubje£t defined, and is 
therefore capable of being employed as a definition 



$ 



Ariftotlfs arrangement is : — 

f Capable of becoming r Definition, 

fubjecls — convertible. ( Property. 



Predicables - 

(^ jecls entire — Inconvertible. ( Accident. 



Incapable of becoming fub- ( Genus, 
jecls entire — Inconvertible. (. . 



154 OUTLINE OF THE 

for fome thinker or other. Logicians have always 
allowed that in our definitions we are bound to con- 
fider, not merely what is abfolutely the explanation 
of the fubjeft, but what our hearers can adopt as an 
explanation. They would not allow that a definition 
which was conveyed in a metaphor, nor one of which 
the words were ftrange or obfolete, was properly a 
definition, becaufe it would not be clear* to the 
hearer. They believed that there was an abfolute 
definition ; but this was to be conveyed with due 
regard to the hearer's needs and attainments. Now 
our reafon for enlarging the limits of definition, is 
that any of the predicates we propofe to include, 
though not the abfolute definition, not the genus and 
difference, may be employed as a definition by fome 
particular perfon, and may to him fulfil the purpofe 
of the beft logical definition which can be given;, 
and therefore ought, if poffible, to be comprehended 
under the fame head. Thus, if I wifti to define 
" honefty," I may fay that it is uprightnefs in tranf- 
a£lions relating to property, that it is probity, that it 
is the beft policy ; and any one of thefe conceptions 
would enable fome of my hearers to identify honefty, 
even though that word had not before occurred in 



* Ariftotle, Top. Z. (vi.) ch. II. mav yap a<ra<p\q to Kara pe- 
ra<popav Xsyof^svov itav yap a<ra<pl<; to (xh eleoBog, 



LAWS OF THOUGHT. 155 

my fpeech, or been fuggefted to their thoughts. If 
there were any one paramount conception, which 
would be to the minds of all a fufficient definition 
of honefty, I mould employ that, and place it in a 
clafs by itfelf. But this is not the cafe. To many 
a humble thinker, " honefty is the beft policy," 
would convey an idea, not adequate indeed but ftill 
diftincT:,* when " honefty is uprightnefs in refpeft to 
tranfaftions connected with property," would be but 
a firing of confufed words. Let us then confider 
definition as any conception which from having pre- 
cifely the fame fphere as another conception, may be 
ufed to afcertain its nature and mark out its limits. 
And the judgment in which definition is predicated^ 
we call a fubftitutive judgment, becaufe it furnifhes a 
predicate identical with the fubjedt. as to fphere or 
extenfion, and therefore capable of being fubftituted 
for it. The fubjecl: of a fubftitutive judgment is 
called alfo the definitum, or conception defined. 

§ 71. Sources of Definition. 

As the fubjedl and predicate of every fubftitutive 
judgment are co-extenfive, they may change places 
in the judgment, fo that the definitum may become 
in its turn a definition. We may define a concep- 

* See p. 94. 



156 OUTLINE OF THE 

tion, by exhibiting in our definition its extenfion, or 
by unfolding its intenfion, or by the fubftitution of 
one fymbol for another, or one fet of marks for an- 
other. It will be found from thefe principles that 
there are fix fources from which definitions mav 
arife. i. From Refolution, when the marks of the 
definitum are made its definition ; as in cc a penfion 
is an allowance for paft fervices." It is not neceflary 
that the marks fhould be completely enumerated — 
that the conception fhould be ftri£tly adequate— but 
only that the marks fhould fuffice for the identification 
of the fubjeft, as belonging to it all and to it alone ; 
fo that Ariftotle's Property would be included in it. 
ii. From Compofition, the reverfe of the laft method, 
in which the definitum, a conception of which the 
component marks are enumerated, ftands fubjeft to 
a definition implicitly containing thofe marks ; as, 
cc thofe who encroach upon the property of others 
are difhoneft." iii. From Divifion, where we define 
the fubjeft by enumerating its dividing members ; as 
" Britons are thofe who dwell in England, Scotland, 
or Wales." All the judgments called disjunctives 
are under this head. iv. From Colligation, the exacft 
reverfe of the laft ; where the dividing members of a 
conception are enumerated in the fubjeft, and the 
divided conception itfelf added to define them ; as, 
" hiftorical, philofophical, and mathematical fciences 



LAWS OF THOUGHT. 



!57 



are the fum (i. e. are all, or equal) of human know- 
ledge." This is the form which Indudtive Judg- 
ments naturally aflume. v. From change of Symbol, 
where both fubjed: and predicate are fymbolic con- 
ceptions, the latter being given as a fubftitute for the 
former on a principle of expedience only ; as " probity 
is honefty." This is the nominal definition of fome 
logic-books, vi. From Cafual Subftitution, where 
one reprefentation is put for another on a principle of 
expedience only, as ferving to recall the marks, which 
both poflefs in common, more readily to the hearer's 
mind ; as cc the fcience of politics is the beft road to 
fuccefs in life \ pleafure is the oppofite of pain." 



o 
C 

o 
U 



TABLE OF DEFINITION. 

- being unfolded, zz i. 



By its In- 
tention (or -< 
Marks) 



By its Ex- 

tention (or H 
Sphere) 



being re-united, rr ii. 
being divided, — iii. 



Jbeing re-united, rz iv, 

of a Symbol, zz v, 
By Acci- 
dental Co- ■< 
incidence L of Notation, == vi. 



Refolution, or 
Definition pro- 
per. 

Compotition. 
Divition. 

Colligation. 

Nominal Defi- 
nition. 

Accidental De- 
finition. 



158 OUTLINE OF THE 

§ 72. Attribute. 
A predicate, the exaft limits of which are not de- 
termined, cannot be ufed to define and determine a 
fubje£t. It may be called an attribute; and conveys, 
not the whole nature of the fubjeit, but fome one 
quality belonging to it. " Metals are heavy;" "Some 
fnakes are venomous;" are judgments in which this 
kind of predicable occurs. 

§ 73. The Common divifion of judgments as to 
Relation. 

The relation in which the fubje£t ftands to the 
predicate in a judgment, whether as co-incident or 
not-coincident with it, we call the doclrine of Re la- 
tton ; as to which we find that predicates are of two 
kinds, fubftitutes, or definitions, and attributes. The 
common account of Relation, which we are bound 
to confider, is fomewhat different. 

Judgments are divided, according to it, into three 
clafles, the Categorical, the Hypothetical, and the 
Disjunctive Judgment. 

The Categorical Judgment is one in which one 
conception is affirmed to belong or not to belong to 
another, as " Men are endowed with confcience," 
" An enflaved people cannot be happy." 

The Hypothetical expreffes feemingly a relation 



LAWS OF THOUGHT. 159 

between two judgments, as caufe and effect, as con- 
dition and conditioned; for example, " If the autumn 
is very dry, the turnip crop is foamy," " If the heart 
is right, fo will the a£Hons be." 

The Disjunctive Judgment exprefTes the relation 
(apparently) of two or more judgments which cannot 
be true together, and one or other of which muft be 
true ; as " Either the Bible is falfe, or holinefs ought 
to be followed ;" or the proverb — " A man is either 
a fool or a phyfician at forty." 

Categorical Judgments are eafily referred to the 
two clafles of fubftitutives and attributives, according 
as their predicates are or are not equal in extenfion 
to the fubje£ts. This kind of judgment prefents little 
difficulty, after the explanations already given. 

Perhaps our readers may be flow to admit that for 
all logical purpofes the hypothetical judgment may 
be treated as a categorical. Yet this is the view to 
which we muft adhere, in common with the beft lo- 
gicians. In the hypothetical, there are not two 
judgments but one. In the example cc If the heart 
is right, the aftions will be fo," we neither fay that 
any one's heart is right, nor that his actions will be ; 
we do not pafs a judgment about either abfolutely, 
but we fay that if the one is, then the other will be. 
So that what we really decide is that there is a con- 
nexion between the two fa£ts ; and the logical copula, 



160 OUTLINE OF THE 

though not expreft there, has its proper place be- 
tween the two claufes, thus ["the cafe, fa£t, or 
notion, of the heart's being right] is [a cafe, fa£l, or 
notion of the a&ions being fo."] But there are 
feveral kinds of hypothetical judgments, which have 
different properties. 

The hypothetical judgment appears, as we have 
faid, as two judgments, the former of them, contain- 
ing the condition, being called the antecedent, and 
the latter, containing the effedt of the condition, 
being called the confequent. In each of thefe there 
are two terms, which would give four in all, if one 
of the terms of the antecedent did not fometimes re- 
appear in the confequent, when the number of dif- 
tinft terms is of courfe but three. Now only five 
arrangements of thefe terms are poffible ; in four of 
which there are but three terms, and in the fifth, four. 

They are 

i. If A is B, A is C 

2. If A is B, B is C 

3. If A is B, C is A 

4. If AisB, CisB 

5. If AisB, C is D. 

The following are examples of thefe formulae. 

1 . If one of the angles of a triangle is a right angle, it muft 

be oppofite to the greater! fide. 

2. If this be poetry, poetry is worthlefs. 



LAWS OF THOUGHT. 161 

3. If animals are creatures with a digeftive cavity, polyps are 

animals. 

4. If virtue is voluntary, vice is voluntary. 

5. If the moon exerts her attractive force in the fame line as 

the fun, the tides are at the higheft. 
The obvious difference between the firft four exam- 
ples and the fifth is, that the fifth alone exprefTes two 
feparate facts, brought together as caufe and effect, 
whilft in all the reft, from the recurrence of a term 
in both claufes, it is impoffible to feparate entirely the 
two things ftated. This leads to the obfervation of 
a real difference in their nature. Without attempt- 
ing to examine the origin of our idea of caufe and 
effect, we may ftate, as a thing generally admitted, 
that all men are accuftomed to regard fome one fact 
as the neceffary refult of another, which they have 
obferved invariably to precede or accompany it ; and 
that they may learn, however different in nature the 
two facts may appear, to identify them fo far as 
invariably to expect the effect where they have ob- 
ferved the caufe. The vibration of a tenfe wire and 
the hearing of a mufical note, are two diftinct facts, 
yet the one caufes the other. The drawing of a 
trigger is a very different fact from the fudden death 
of a healthy man ; yet every one knows that under 
certain circumftances the one will infallibly caufe the 
other. The revolution of the moon has fo little 
apparent connexion with the fpring and neap tides, 

M 



1 62 OUTLINE OF THE 

that it would be long before men obferved what is 
really the cafe, that the pofition of the moon influ- 
ences the tide's fluctuations. Experience obferves 
that events happen together, or in a clofe fucceflion, 
and the mind, after adequate obfervations, connects 
them by its idea of caufe. Whether this idea be alfo 
a part of the experience, or one of the primitive con- 
stituents of the mind itfelf, even as the eye is a con- 
stituent part of the body, is a queftion much debated ; 
but it need not occupy us. We have to remark that 
two fails, which do not refemble one another, be- 
tween which perhaps we once faw no connexion, 
may be infeparably linked together in our minds, as 
a caufe and an effeit. And when the connexion 
between them is ftated, in a hypothetical (that is, a 
conditional) judgment, the truth of the ftatement will 
entirely depend upon the correitnefs of our obferva- 
tion, fince there can be nothing in the ftatement 
itfelf to ferve as a criterion of its truth. In " If A 
is B, C is D" we have no teft but the application of 
our idea of caufe and effeit to the fails for which 
thefe letters ftand. But in " If A is B, A is C," we 
appeal, not to the idea of caufe, but to a categorical 
judgment of which we have the materials before us. 
« If A is B, A is C" will be true provided " All B 
is C" be true. " If this is an equilateral triangle, it 
is alfo an equiangular" muft be tried by the rule 



LAWS OF THOUGHT. 163 

u All equilateral triangles are equiangular." Here 
is no notion of caufe ; but a ftatement of a rule, with 
the fuppofition that fome one cafe comes under it. 
It really means, not that one event is caufed by ano- 
ther, but that a conception has certain marks; which 
is the function of the categorical judgment. 

All judgments apparently hypothetical, but having 
three terms only, may be reduced to categoricals by 
leaving out the term that is repeated, and ufing the 
other two for fubjeft and predicate. Thus " If this 
be poetry, poetry is worthlefs" becomes " This (po- 
etry) is worthlefs :" and " If virtue is voluntary, vice 
is voluntary/' means that " Virtue, (in fo far as per- 
tains to the control of the will) is the fame as vice." 
But as they have the conditional form, they may alfo 
be reduced to categoricals in the mode already de- 
fcribed ; — a The cafe of virtue being voluntary is a 
cafe of vice being voluntary." The conditional par- 
ticle if means in judgments of this kind " if it mould 
prove that — or, be granted that," fince the fafts exift 
already, and the fuppofition refers to our knowledge 
of them. But in the true conditional the " if" fig- 
nifies " if it occurs that," fince the fa£t muft come 
about to neceffitate the occurrence of another fact. 

But whilfl: conditional judgments differ eflentially 
from categoricals, the former affirming the caufal 
connexion between two diftmCt facts,, and the latter 



1 64 OUTLINE OF THE 

declaring that a thing or clafs of things has fome 
property, there is alfo a fufficient fimilarity to admit 
of their being identified, for logical purpofes. Both 
alike affirm the invariable connexion of their two 
terms. By cc All the tiffues of the body continually 
decay and are reproduced," is meant that wherever 
one of the tiffues of the human body exifts, decay 
and reproduction are going on, and cannot be abfent : 
and in like manner, by " If the moon's attraction 
a£ts againfl: that of the fun, the tides are low" is 
meant that whenever thefe two heavenly bodies are 
found in the fuppofed pofition, we find a particular 
ftate of the tides. In both cafes, one thing is affirmed 
to be an accompaniment of another. In the cate- 
gorical, a thing has the mark expreft by the predi- 
cate ; and in the conditional, a fa£t has another fa6t 
for its mark. In the example given of the former 
kind of judgment, we affirm that without the notion 
of decay and reproduction, our notion of the tiffues 
of the body would be wrong and incomplete : in the 
other example, that our notion of that pofition of the 
heavenly bodies would be incomplete, if we did not 
take into view its influence on the tides. Logic, wil- 
ling to fimplify her formulae, and to leave the exami- 
nation of the idea of caufe and effe£t to Metaphyfics, 
reduces the conditional to the fame rules as the cate- 
gorical. The formula " The cafe, fa£t, or notion of 



LAWS OF THOUGHT. 165 

this exifting, is, a cafe, fa£t, or notion of that exift- 
ing" is fufficient for the reduction of any conditional 
to a categorical. For true conditionals, i. e. thofe 
where the fuppofition relates to the occurrence of 
fadls, not to our knowledge of fa£ts, we fhall gene- 
rally fay " The faSf of his being" &c. ; for the other 
kinds, " The notion" &c. But fome variations are 
admiffible. Thus, recurring to our examples, we 
may fay, 

1. The cafe of one angle of a triangle being a rectangle — is — 

a cafe of its being oppofite to the greater!: fide. 

2. The admhTion that this is poetry — would be an admiflion 

that poetry is worthlefs. 

3. The ftatement that animals are creatures with a digeftive 

cavity — implies — that polyps are animals. 

4. The notion that virtue is voluntary — implies — the notion 

that vice is voluntary. 

5. The fact that the moon exerts her attractive force in the 

fame line as the fun — implies — the fact that the tides 
are at the higheft. 

But let it be noticed that the four firft examples 
contain the materials not fo much of a judgment, as 
of a perfect argument, of which one of the judgments 
isfuppofed to be true. 

1. Every right angle of a triangle is oppofite the greater! fide, 
This angle is a right angle ; 
Therefore it is oppofite to the greaterl fide. 



1 66 OUTLINE OF THE 

2 . This poetry is worthlefs, 

This poetry is all poetry (i. e. is a fair fample of every 

kind) ; 
Therefore all poetry is worthlefs. 

3. Animals = creatures with a digeftive cavity, 

Polyps have this ; 
Therefore they are animals. 

4. Virtue is voluntary, 

Vice (as far as the will goes) is the fame as virtue 5 
Therefore vice is voluntary. 

Conditionals may appear either as fubftitutive or 
attributive judgments. If they fet forth fome caufe 
which not only produces a given effecl, but is the 
only caufe that does fo^ they belong to the former 
clafs. " If the moon comes between the fun and 
the earth, the fun will be eclipfed" — is a judgment 
of this kind, for there is no other caufe which pro- 
duces that effeft : and therefore we may either fay 
" All cafes of the moon's coming between the fun 
and the earth— are — cafes of the fun's being eclipfed" 
or the fimple converfe cc All cafes of the fun's being 
eclipfed — are — cafes of the moon's coming between 
the fun and the earth." But where the caufe ftated 
is only one of feveral which might have produced 
the effecl:, — as in " If it rains, the flower beds will 
be wet," where the fame effe£t would be produced 
by the falling of dew, or the ufe of the watering-pot, 
— we cannot employ the fimple converfe, for the 



LAWS OF THOUGHT. 167 

predicate is wider than the fubjecT:. We may fay 
" All cafes of its having rained are cafes of the 
flower-beds being wet," but obvioufly not " All cafes 
of the flower-beds being wet are cafes of its 'having 
rained." Thefe are attributives. 

Disjunctive judgments may all be referred to the 
head of fubftitutives ; for the fphere of the predicate 
is juft equal to that of the fubjecT:, the latter being a 
conception, and the former the fame conception lo- 
gically divided (§ 57.) In " Either Shakfpeare is 
wrong, or Richard III. was a monfter," our mean- 
ing may be exprefled thus — " The poflible cafes in 
this matter are that Shakfpeare is wrong, and that 
Richard III. was a monfter ;" which is a fubftitutive 
judgment. The real premifs in a disjunctive argu- 
ment is not the disjunctive judgment itfelf, but, as will 
be fliown, a certain immediate confequence from it. 

§ 74. DoSfrine of Quantity ', or of the extenfon 
ofthefubjeft in a judgment. 

A judgment is either about the whole of a concep- 
tion, as "All ftars mine ;" and this we call a univerfal 
judgment : or about part of a conception, as " Some 
lakes have an outlet," and this is a particular judg- 
ment ; or about an intuition, as u Northumberland 
Houfe is near Charing Crofs," and this is a Angular 
judgment. 



168 OUTLINE OF THE 

For logical purpofes we may regard all fingulars as 
univerfals, becaufe they agree in bringing in the whole, 
and not a part, of their fubjeft. So that as to Quan- 
tity, judgments are either univerfal or particular^ 



* See Wains' 1 Logic. Thefts I. Further diftin&ions of judg- 
ments as to Quantity have been brought in by the acutenefs 
of logicians, which for philofophical purpofes are not very im- 
portant. The judgment — " Moll men are prejudiced"" cannot, 
it is argued, be confidered as particular, for it implies not only 
that fome men, but more than the half 'of mankind are preju- 
diced. Thefe are termed plurative judgments ; and will be 
mentioned again in examining the fyllogifm. To ProfefTor 
De Morgan belongs the merit of recalling attention to them 3 
and in his elaborate and acute " Formal Logic/' p. 325, he 
inferts Sir W. Hamilton's remark upon the ufe of them, that 
" all that is out of claflification — all that has no reference to 
genus and fpecies, is out of Logic, indeed out of Philofophy 5" 
that Philofophy feeks to know whether all or fome or none of a 
fubjecl: comes into a predicate, but not whether much or little, 
for " Philofophy tends always to the univerfal and neceffary," 
to v*hich this diftinclion does not feem to belong. At the fame 
time the plurative judgment deferves attention, as being a pof- 
fible mode, and as one more proof of the incompletenefs of the 
do6trine of the fyllogifm as commonly taught. 

In the fame work (p. 142), another clafs of proportions 
is mentioned, called the " numerically definite proportion, 
where the number of objecls both of the fubjecl: and predicate 
is known and fpecified. The fame objection and defence 
would apply to them as to the plurative judgments ; only that 
their practical ufe feems even lefs, and it is difficult even to in- 
vent an example likely to occur. 



LAWS OF THOUGHT. 169 

§ 75. Doclrine of Quality , or the agreement or 
difagreement offubjecl and predicate. 

Where a judgment exprefles that its two terms 
agree, it is called Affirmative ; as, All planets move 
in an elliptic orbit ; where it expreffes their difagree- 
ment, it is termed negative ; as, No human know- 
ledge is perfect. This part of the judgment is its 
Quality. Although the negative particle is not al- 
ways connected with the copula, but may appear in 
other parts of the fentence, in every real negative 
judgment it belongs only to the copula. The two 
terms are given, and the queftion always is whether 
is or is-not mall be the connecting link between them. 

But by removing the negative fign from the copula, 
and attaching it to the predicate, we may turn the 
judgment into an affirmative of a peculiar kind, fome- 
times called an indefinite,* which is equivalent in fig- 
nification to the negative. Inftead of, No human 
knowledge is perfe£t, we may fay with equal truth, 
All human knowledge is »0«-perfe£t 5 or imperfe£k. 
This licenfe is founded on the law that it amounts to 
the fame thing whether we fay that our fubjecT: is 
(hut out from fome pofitive conception or included 
in the cognate privative, for any given fubjeit. what- 

* By Wolff, Phil. Rat. § 209, and Kant, Logik § 22. 



170 OUTLINE OF THE 

ever muft be found in one of the two (p. 170). But 
for logical purpofes thefe indefinite judgments may, 
without inconvenience, be confidered as affirmatives. 
To diftinguifh between negative judgments and 
fuch as are fo only in appearance, we muft confider 
whether the fign of negation, not , is meant to affe£t 
the copula, or whether it really belongs to one of 
the terms. In, " Not to fubmit would be mad- 
nefs," there is no negation, though the fign of it is 
expreffed. 

§ 76. DoSfrine of Modality. 

The degree of certainty with which a judgment is 
made and maintained, is called its modality; as being 
the mode^ or meafure, in which we hold it to be true. 
We affirm with very different degrees of affurance, 
the two judgments, that " An equilateral triangle is 
equiangular" and that " Zeno of Elea was the in- 
ventor of dialectic ;" fince we can prove the former 
to demonftration, whilft doubts may be entertained 
as to the evidence on which the latter refts. Opi- 
nions differ as to the place which this do£lrine ought 
to hold in Logic. Not without hefitation, it is here 
excluded from pure, to be difcuffed in applied Logic, 
on the ground that the modality of a judgment is not 
part of itfelf, and does not belong to the copula, — as 
feems to be fhown by the fa£t that the degree of 



LAWS OF THOUGHT. 171 

certainty about the fame judgment fluctuates in the 
mind of the fame perfon at different times, and, ftill 
more, in different perfons, the mode of expreffion 
remaining unaltered. 

§ 77. Dijiribution of Terms in Judgments. 

Univerfal judgments diftribute, i. e. introduce the 
whole of, their fubjeft; particulars do not. In "All 
the fixed ftars twinkle" and " No man is wife at all 
times," it is obvious that we are fpeaking of the 
whole of the fixed ftars, and of men, refpe£tively ; 
and therefore each term is diftributed. 

Negative judgments diftribute the predicate. If 
" No minerals are nutritious for animals" is afferted, 
it means that nothing which is nutritious for animals 
can have the properties of minerals ; and fo the term 
" nutritious for animals" is diftributed; and if we 
fuppofe that only fome nutritious things are afferted 
not to agree with minerals, it would follow that fome 
other nutritious things might agree with, u e> might 
be, minerals, fo that we might fay at the fame time — 
" No minerals are nutritious for animals" and "Some 
minerals are nutritious for animals;" whereas we 
know that we meant by the former judgment to ex- 
clude the poflibility of our receiving the latter. If 
the predicate of a negative is not diftributed, it can 
have no real negative power; for if the fubjedt, is only 



172 OUTLINE OF THE 

excluded from one part of the predicate, it may be 
included in fome other part. 

Substitutive judgments diftribute the predicate. 
Since the predicate in them is ufed to define the fub- 
je£t, or in other words to mark its exadt limits, it 
muft itfelf be definite, and therefore the whole of it 
muft be given, otherwife the uncertainty as to what 
part was meant, would make it ufelefs for definition. 

We may here remark that an ambiguity attaches 
to fome particles which have important duties in 
Logic. The copula is means always exijls* but 
when ufed in a proposition, it exprefies an existence 
modified or limited by the predicate ; when employed 
alone, it exprefies abfolute exiftence, u e. that the 
fubjeit is among the clafs of really exifting things. 
Upon this variation a well-known fallacy! was found- 
ed ; that of arguing that becaufe " Ptolemy is dead" 
(/. e. only exifts to us in the way that a dead perfon 
can, by a remembered or traditionary notion) there- 
fore " Ptolemy i$" (/. e. has an aftual exiftence 
among other living perfons,) which is a very different 
ftatement. 

Again the word all in its proper logical fenfe 
means " each and every ," but it ftands fometimes 

* See however Waitz, on Organ. 16, a, 12, for the fenfe 
of the copula in Ariftotle. 

f Ariftotle , de Soph. Elench. ch. v. iii. Tauchnitz. 



LAWS OF THOUGHT. 173 

for " all taken together — " " All thefe claims upon 
my time overpower me." Hence may arife an am- 
biguity ; inftead of the all in its logical ufe, we may 
put every ; but to exercife the fame liberty with the 
other fenfe of it would be abfurd. The example 
given could not mean " Every fingle claim upon my 
time overpowers me." 

The word fome is likewife the caufe of confufion, 
in its logical ufe. In what fenfe is the " fome" of a 
particular proportion to be underftood ? Does it 
mean " Some, we know not how many," or "A cer- 
tain number, which we may have in our thoughts" ? 
Suppofe that hiftorical reading leads to the conviction 
that " Some democratic governments have ended in 
a tyranny," it may be doubtful whether this refult 
includes precifely thofe democracies which we have 
found in our refearches were confummated by def- 
potifm, and no others, in which cafe the conception 
in our minds is definite and precife, though conveyed 
in an indefinite expreffion, or only exprefles that 
this has occafionally happened to democracies, pof- 
fibly to others befides thofe which we have ftudied, 
in which cafe the conception " fome democracies" 
would be purely indefinite. The word appears to be 
employed in the two fenfes of " Some or other," 
and " Some certain," in common language ; and it 
becomes a queftion in which fenfe it is to be regarded 
in Logic. 



174 OUTLINE OF THE 

Now the different fteps in attaining knowledge 
are marked by the acquirement of new laws or rules, 
that is to fay, of univerfal judgments, expreffing 
that to the whole of a given clafs of things or 
fafts, fome mark or property belongs. And where- 
ever a definite number of things is afcertained to 
pofTefs a mark, it is the tendency of the mind to 
fet them apart from other things that moft refem- 
ble them, by fome name, which may ftand for them 
both in thought and fpeech, for the fake of mak- 
ing the ftatement univerfal. If by " Some demo- 
cracies have ended in defpotifm," we mean fimply 
to afTert that in three or four countries, with the 
hiftory of which we are familiar, and which we could 
name, this refult has occurred, the ftatement is 
really univerfal, becaufe our fubjeft is only a fpecies 
arbitrarily formed of the genus " democracies ;" and 
we ought to fay " The democracies (three or four) 
whofe hiftory we have traced." But as our having 
ftudied them is not of importance enough to found a 
diftin£lion upon, a univerfal afTertion of this kind 
would have no philofophical value ; and by " Some 
democracies end in defpotifm" we fhould mean to 
declare that in trying to find the agreement between 
thefe two terms, we had not fucceeded in eftablifti- 
ing the rule, the univerfal judgment, but that a par- 
tial agreement had appeared, the extent of which, 
though it was difcovered from fome particular cafes, 



LAWS OF THOUGHT. 



*7S 



was not, fo far as we knew, limited to them, but 
remained thoroughly indefinite. Every term then 
which, though indefinitely exprefled, refers to a de- 
finite clafs of things, mould be rendered definite. 
Wherever the things denoted by the fubjeft are really 
definite, as having fome marks that group them in a 
fmaller clafs by themfelves, fcience requires that in- 
ftead of appearing as part of a larger clafs, they mould 
have their own name and pofition. 



SUMMARY OF THE ANALYSIS OF JUDGMENTS. 



,-C <L> 

Quantity * g 



Quality 



> <u J 
O « 



o 




4J ■* 


r£ 


c 


*■* 


o 




a 




W) 


<fc 


P 


.& M 


•— > 


42 <U 


O 


8 -a 


a 

Sh 

o 


Relation ^ ?3 


o 




0) 


.5 <u 


3 


-> E 


CS 


£ 5J3 


fc 


si 


u 




-«5 


B9 


H 


ri 



Unlverfal — where the whole fubjecl: is 
joined to the predicate, 

or Particular — where part of the fub- 
jecl: is joined to the predicate. 

Affirmative — where the predicate is 
decided to agree with the fubjecl:, 

or Negative — where the predicate is de- 
cided not to agree with the fubjecl:. 

Attributive — where an indefinite (i. e. 
undiflributed) predicate is affigned 
to the fubjecl,. 

or Subftitutive — where a definite (i. e. 
diftributed) predicate is affigned to 
the fubjecl, which may be fubftituted 
for it, and ferve as its definition. 



176 OUTLINE OF THE 



§ 78. Table of all the Judgments. 

The following table contains examples of the fix 
kinds of judgments, with their Quantity, Quality 
and Relation exprelTed, and the vowels which may 
conveniently be ufed as fymbols of them. 

Sign. Example. Quant. Qual. Rel. 

A. All plants grow. Univ. Affirm. Attrib. 

E. No right action is inexpedient. Univ. Neg. 

I. Some mufcles act without our volition. Part. Affirm. Attrib. 

O. Some plants do not grow in the tropics. Part. Neg. 

U. Common fait is chloride of fodium. Univ. Affirm. Subfti. 

Y. Some ftars are all the planets. Part. Affirm. Subfti. 

An infpe&ion of the table will ftiow that of the 
fix judgments there are three of univerfal and three 
of particular quantity ; that there are four of affirm- 
ative and two of negative quality ; that there are two 
of attributive and two of fubftitutive relation, whilft 
the two negatives, as denying that either relation fub- 
fifts between the fubjecT: and predicate, are undeter- 
mined as to relation. The vowels in the firfl: column 
are very ufeful in abbreviating the proceffes of Logic ; 
for inftead of faying that a given judgment is a uni- 
verfal affirmative judgment, it is fufficient to fay that 
it is an A, which conveys to one converfant with 
Logic, the fame meaning. The laft example, of Y, 
is given in the words beft adapted to fhow the diftri- 



LAWS OF THOUGHT. 177 

bution of its terms ; but in practice it would pro- 
bably occur as u Stars include the planets," which 
has precifely the fame import. But this form of 
judgment is feldom ufed,* becaufe, the fubjecl: being 
the principal notion in every judgment, it is unnatu- 
ral to put an indefinite (i. e. undiftributed) conception 
in the principal place, and a definite (i. e. diftributed) 
conception in the place of fecond importance. That 
notion of which we had the whole before us, would 
naturally occur firft ; and this, it feems, is the pfycho- 
logical principle on which " All planets are ftars" is 
a more obvious and natural judgment than its con- 
verfe " Some ftars are all planets." Nor is the pre- 
dicate of Y ftriclily definitive, fince it only ferves 
that purpofe for a part of the fubje£l. 

§ 79. Table of judgments according to Sir W. 
Hamilton. 

To the fix judgments juft given, a very diftin- 
guifhed logician adds two. Extending the doctrine 
of diftribution, he fays that in negative judgments, as 
well as in affirmative, we may fpeak of— the whole 
of both terms — part of both terms — the whole of 

* The old logicians would have called it, probably, an "/»- 
ordinata propojltio" or unnatural proportion — Keckermanni 
Log. B. 11. § i. cap. 1, not quite upon the fame grounds. Comp. 
Arifl. An. Poft. i, xxii. 35 and Zabarella upon it, p. 909. 

N 



178 OUTLINE OF THE 

the fubjeft and part of the predicate — part of the 
fubject and the whole of the predicate ; fo that there 
are four kinds of affirmatives and four of negatives. 
Putting X and Y to ft and for any fubje£fc and predi- 
cate, we may exhibit them thus : — 



Sign 


Affirmatives. 


Negatives. 


Sign. 


U. 


All X is all Y 


No X is Y. 


E. 


I. 


Some X is fome Y 


Some X is not fome Y. 


00* 


A. 


All X is fome Y 


No X is fome Y. 


V. 


Y. 


Some X is all Y 


Some X is no Y. 


0. 



On comparing this table with that given in the 
laft fe£tion, it will be found that with the exception 
of the two negatives marked y and &>, each judgment 
here has a counterpart there. Why have we ven- 
tured, in accordance with the practice, it is believed, 
of all logicians, to exclude thefe two ? 

The anfwer is, that whilft Sir William Hamilton 
gives a table of all conceivable cafes of negative pre- 
dication, other logicians have only admitted aclual 
cafes. It is not inconceivable that a man fhould 
fay " No birds are fome animals," (the n of the Table) 
and yet fuch a judgment is never actually made, 
becaufe it has the femblance only, and not the power, 
of a denial. True though it is, it does not prevent 
our making another judgment of the affirmative kind, 
from the fame terms ; and " All birds are animals" 
is alfo true. Though fuch a negative judgment is 



LAWS OF THOUGHT. 179 

conceivable, it is ufelefs ; and feeling this, men in 
their daily converfation, as well as logicians in their 
treatifes, have profcribed it. — But the fruitleffnefs of 
a negative judgment where both terms are particular 
is even more manifeft ; for " Some X is not fome 
Y " is true, whatever terms X and Y ftand for,* and 
therefore the judgment, as prefuppofed in every cafe, 
is not worth the trouble of forming in any particular 
one. Thus if I define the compofition of common 
fait by faying " Common fait is chloride of fodium," 
I cannot prevent another faying that " Some common 
fait is not fane chloride of fodium," becaufe he may 
mean that the common fait in this falt-cellar is not 
the chloride of fodium in that. A judgment of this 
kind is fpurious upon two grounds ; it denies nothing, 
becaufe it does not prevent any of the modes of 
affirmation ; it decides nothing, inafmuch as its truth 
is prefuppofed with reference to any pair of concep- 
tions whatever. In a lift of conceivable modes of 
predication, thefe two are entitled to a place. t 

* Except of courfe they reprefent individuals ; and all that 
could be inferred from fiich a judgment would be that its terms 
were general, not individual — conceptions, not intuitions. Even 
this however is provided for, as we know from their being par- 
ticular, that they muft be capable of divifion, and therefore 
general. " Some Nicias" could only be faid with propriety, 
if there were feveral men bearing that name. 

f To my objection, that the two weaker negatives have never 



180 OUTLINE OF THE 

§ 80. Import of Judgments. Extenjion and 
In ten/ion . Nam ing. 

Upon the examination of any judgment which 
appears to exprefs a fimple relation between two 
terms, we fhall find it really complex, and capable 
of more than one interpretation. " All ftones are 
hard" — means in the firfl: place that the mark, hard- 
nefs, is found among the marks or attributes of all 

occurred in the examination of logical examples, Sir William 
Hamilton replies in the Athenaum (in a letter dated February 
25, 1 8 51) as follows : — "The thorough-going quantification of 
the predicate (on demand) in its appliance to negative propo- 
rtions, is not only allowable, is not only fyftematic, is not only 
ufeful, — it is even indifpenfable. For to fpeak of its very 
weaken 1 form, that which I call parti-partial negation, "fome 
— is notfome $ " — this (befides its own ufes) is the form which we 
naturally employ in dividing a whole of any kind into parts : 
— " Some A is notfome A" And is this form — that too in- 
continently, — to be excluded from logic ? — But again, (to prove 
both the obnoxious propofitions fummarily and at once ;) — 
what objection, apart from the arbitrary laws of our prefent 
logical fyftem, can be taken to the following fyllogiim ? — 

' All man is fome animal, 

Any man is not (no man is) fome animal', 

Therefore fome animal is not fome animals 

Vary this fyllogifm of the third figure to any other 5 it will al- 
ways be legitimate by nature, if illegitimate to unnatural art. 
Taking it, however, as it is : — the negative minor premife, with 
its particular predicate, offends logical prejudice. But it is a 



LAWS OF THOUGHT. 181 

ftones ; and in this fenfe of the judgment, the pre- 
dicate may be faid to be contained in the fubjecT:, for 
a complete notion of ftones contains the notion of 
hardnefs and fomething more. This is to read the 
judgment as to the intenfion (or comprehenfion) of 
its terms (p. 105). Where it is a mere judgment of 
explanation, it will mean M the marks of the predicate 
are among what I know to be among the marks of 
the fubjecT: : " but where it is the expreffion of a new 

propofition irrecufable ; both as true in itfelf, and as even prac- 
tically neceffary. Its converfe, again, is technically allowed; 
and no propofition can be right of which the converfe is wrong. 
For to fay (as has been faid from Ariftotle downwards,) that 
a particular negative propofition is inconvertible, — this is 
merely to confefs that the rules of logicians are inadequate to 
the truth of logic and the realities of nature. But this inade- 
quacy is relieved by an unexclufive quantification of the pre- 
dicate. A toto-partial negative cannot, therefore, be refufed. 
— But if the premifes are correct, fo likewife mult be the con- 
clufion. This, however, is the doubly obnoxious form of a 
parti-partial negative : 

1 Some animal (man) is not fame animal (fay, brute).' 

" Nothing, it may be obferved, is more eafy than to mifapply 
a form ; nothing more eafy than to ufe a weaker, when we are 
entitled to ufe a ftronger propofition. But from the fpecial 
and factitious abfurdity thus emerging, to infer the general 
and natural abfurdity of the propofitional form itfelf, — this is, 
certainly, not a logical procedure." 

This alfo occurs, with a few verbal alterations, in Hamilton's 
Difcuffions in Philofophy, &c. p. 163. 



182 OUTLINE OF THE 

ftep in our inveftigation, of an acceffion of know- 
ledge, it muft mean "the marks of the predicate are 
among what I now find to be the marks of the fub- 
jeft." # 

Both fubje£t and predicate however not only im- 
ply certain marks, but reprefent certain fets of ob- 
je£ts. When we think of " all ftones," we bring 
before us not only the fet of marks — as hardnefs, fo- 
lidity, inorganic ftrudture, and certain general forms 
— by which we know a thing to be what we call a 
ftone, but alfo the clafs of things which have the 
marks, the ftones themfelves. And we might inter- 
pret the judgment " All ftones are hard" to mean 
that " The clafs of ftones is contained in the clafs of 
hard things." This brings in only the extension of 
the two terms ; according to which, in the example 
before us, the fubje£t is faid to be contained in the 
predicate. Every judgment may be interpreted from 
either point of view ; and a right underftanding of 
this do£lrine is of great importance. Let it be no- 
ticed, againft a miftake which has been re-introduced 
into logic, that all conceptions, being general^ repre- 
fent a clafs, and that to fpeak of a u general name" 
which is not the name of a clafs, is a contradiction 
in terms. But this is very different from aflerting 

* See next §. 



LAWS OF THOUGHT. 183 

that a clafs of things correfponding to the conception 
actually exifts in the world without us. The con- 
ceptions of giant, centaur and firen are all of claflfes; 
but every one knows, who realizes them, that the 
only region in which the dalles really exift, is that 
of poetry and fiction. The mode of exiftence of the 
things which a conception denotes is a mark of the 
conception itfelf; and would be expreffed in any 
adequate definition of it. It would be inefficient to 
define " Centaurs" as a fet of monfters, half-men 
and half-horfes, who fought with the Lapithae, fo 
long as we left it doubtful whether they affually 
lived and fought, or only were feigned to have done 
fo ; and by fome phrafe, fuch as " according to Ovid" 
or " in the Mythology" we fhould probably exprefs 
that their actual exiftence was not part of our con- 
ception of them. 

The judgment felected as our example contains 
yet a third ftatement. We obferve marks \ by them 
we fet apart a clafs ; and laftly we give the clafs a 
name or fymbol, to fave the trouble of reviewing all 
the marks every time we would recall the conception. 
" All flones are hard" means that the name hard 
may be given to every thing to which we apply the 
name ftones. 

All judgments then may be interpreted according 
to their Intenfion, their Extenfion, and their appli- 



184 OUTLINE OF THE 

cation of names or defcriptions ; as the following ex- 
amples may help to {how. 

A. " All the metals are conductors of electricity" means 

Intenfion. The attribute of conducting electricity be- 
longs to all metals. 
Extension. The metals are in the clafs of conductors 

of electricity. 
Denomination. The name of conductors of electricity 
may be applied to the metals (among other things) .* 

E. " None of the planets move in a circle" means 

Intenfion. The attribute of moving in a circle does 

not belong to any planet. 
Extenfion. None of the planets are in the clafs (be it 

real, or only conceivable) of things that move in 

a circle. 
Denomination. The defcription of things that move 

in a circle cannot be applied to the planets. 

I. " Some metals are highly ductile" means 

Intenfion. The mark of great ductility is a mark of 
fome metals. 

Extenfion. Some metals are in the clafs of highly duc- 
tile things. 

Denomination. The name of highly ductile things, 
may be applied to fome metals. 

O. " Some lawful actions are not expedient" means 

Intenfion. The attribute of expediency does not be- 
long to fome lawful actions. 



* "Among other things." This qualification is required 
by the rules of diflribution, for metals are only fome conduc- 
tors. 



LAWS OF THOUGHT. 185 

Extenfion. Some lawful actions do not come into the 

clafs of expedient things. 
Denomination. The name of expedient cannot be given 

to fome lawful a£Kons. 

U. "Rhetoric is the art of perfuafive fpeaking" means 

Intenfion. The attributes of the art of perfuafive 

fpeaking, and of Rhetoric, are the fame. 
Extenfion. Rhetoric is co-extenfive with the art of 

fpeaking perfuauvely. 
Denomination. " The art of perfuafive fpeaking, 1 ' is 
an exprerTion which may be fubftituted for Rhetoric. 

Y. " The clafs of animals includes the polyps" means 

Intenfion. The attributes of all the polyps belong to 

fome animals. 
Extenfion. The polyps are in the clafs of animals. 
Denomination. The name of polyps belongs to fome 

animals. 

§ 81. Explicative and Ampliative "Judgments. 

Some judgments* are merely explanatory of their 
fubjecT:, having for their predicate a conception which 
it fairly implies, to all who know and can define its 
nature. They are called explicative (or analytic) 
judgments, becaufe they unfold the meaning of the 
fubjecT:, without determining anything new concern- 
ing it. Though they cannot be faid to augment our 
knowledge of the fubjecT:, the habit of thinking of 
things without realizing all their marks, is fo com- 

* Kant, Logik, §36, and Prolegomena, § 2. Alfo, for the 
names here adopted, Sir W. Hamilton in ReicTs Works. 



186 OUTLINE OF THE 

mon, that judgments in which the marks are predi- 
cated anew are ufeful to revive our remembrance of 
them ; whilft they are indifpenfable in explaining to 
others the nature of our fubjecl:, of which they may 
not have an adequate notion. If we fay that cc all 
triangles have three fides," the judgment is explica- 
tive ; becaufe " having three fides" is always im- 
plied in a right notion of a triangle.* 

Judgments of another clafs attribute to the fub- 
je£t fomething not directly implied in it, and have 
been called ampliative, becaufe they enlarge or in- 
creafe our knowledge. They are alfo called fynthe- 
tic, from placing together two notions not hitherto 
ailbciated. For example — u All bodies poffefs power 
of attraction" is an ampliative judgment; becaufe we 

* Such judgments, as declaring the nature or effence of the 
fubje6t, have been called " eil'ential proportions." Mill's Lo- 
gic, B. i« ch. vi. It is however a mimomer to call them all 
"identical proportions." "Everyman is a living creature 1 ' 
would not be an identical proportion unlefs " living creature" 
denoted the fame as " man ;" whereas it is far more extenfive. 
Locke underftands by identical proportions only fuch as are 
tautologous — "by identical proportions, I mean only fuch 
wherein the fame term, importing the fame idea, is affirmed 
of itfelf." (Hum. Under. IV. viii. 3.) But he condemns the 
ufe of what we have called analytic judgments likewife, 
(Hum. Under. IV. viii. 4.) as adding nothing to real know- 
ledge : he would probably admit them as explanatory propo- 
rtions. 



LAWS OF THOUGHT, 187 

can think of bodies without thinking of attraction as 
one of their immediate primary attributes. But if 
our knowledge of any object were complete, we 
fhould conceive it invefted with all its attributes, 
and no ampliative judgments would be required. 

We muft diftinguifh between explicative and 
tautologous judgments. Whilft the explicative dis- 
play the meaning of the fubjecl:, and put the fame 
matter in a new form, the tautologous only repeat 
the fubject, and give us the fame matter in the fame 
form, as " Whatever is, is." " A fpirit is a (pint." 
Whether in thinking or in teaching, the tautologous 
judgments areufelefs. # 

* Kanty Logik, § 37. Locke, Hum. Under, iv. viii. 2. — 
They may accidentally, and by a particular emphafis, become 
the vehicles of emotion or rebuke. The " Seniation is fenfa- 
tion," of Dr. Joh/ifon, means " One cannot help feeling." 
So too the obvious analytic judgments, " A negro has a foul, 
pleafe your honour/ 1 of Siemens Corporal, and " He has no 
wife M of the agonized Macduff, convey a pathos from their 
accidental ufe, and from the train of judgments they fuggeft, 
but difdain to exprefs, which their mere logical import does 
not account for. 



OUTLINE OF THE LAWS 
OF THOUGHT. 

PART III. 
SYLLOGISM. REASONING. 

O (jlev yap (TuXXoyicrfjLQg ek tlvcov efti teQevtgw, oq<tte 
Xeysiv STepov tl e£ avdyKY\<; rSv ksi/jlevoov oia tuv kei/aevoqv. 

Aristotle. 



SYLLOGISM. REASONING. 




§ 82. Syllogifm. 

^^j ^gp HEN the ftate of our knowledge does 
not warrant us in judging at once whe- 
ther two conceptions agree or differ, 
we feek for fome other judgment or 
judgments, that contains the grounds for our coming 
to a decifion. This is called reafoning, which may- 
be defined " the procefs of deriving one judgment 
from another/' The technical name for that one 
fingle ftep of the procefs, of which the longeft chains 
of reafoning are but the repetition, is fyllogifm, (or 
computation,) a word which has acquired its prefent 
fenfe from the refemblance between computation 
proper, u e. gathering the refults of a fum, and that 
gathering of the refult of other judgments that we 
call reafoning. A fyllogifm has been defined " A 
fentence or thought in which, from fomething laid 
down and admitted, fomething diftinct from what 
we have laid down follows of neceffity. # The form 



* Arijlctle, Pri. An. 1. i. I fay "a fentence or thought" 



192 OUTLINE OF THE 

or effence of a fyllogifm therefore confifts, not in the 
truth of the judgments laid down or of that which 
is arrived at, but in the produ6Hon of a new and 
diftinft judgment, not a mere repetition of the 
antecedents, the truth of which cannot be denied 
without impugning thofe we have already accepted 
for true. 

The new judgment which is to be drawn, and 
which gives occafion for the reafoning procefs, is 
called, before proof is found, the queftion or problem, 
and after proof the conclufion. The judgments 
ufed to eftabliih the conclufion are termed the pre- 
mises; and the connexion between the premiffes and 
conclufion, that entitles us to gather the one from 
the other, is the confequence ; as appears from the 
phrafes " by confequence," " confequently," fo often 
employed in argument. Sometimes the conclufion, 
as following, "by confequence" has itfelf the name 
of confequence, although confequent would be more 
ftriftly correft. Latin writers have applied the 
names complexio and connexlo to the fame part of the 
fyllogifm. 

becaufe "koyoq means both ratio and oratio. The words " laid 
down and admitted" have no exclufive reference to difputa- 
tion, for we may lay down judgments for our own ufe alone, 
when there is no difputant in the cafe. Trendelenburg and 
JVaitz, on this paflage. 



LAWS OF THOUGHT. 193 

§ 83. Immediate and Mediate Inference. 

In fome cafes we are unable to decide that the 
terms of the queftion agree with or differ from one 
another, without rinding a third, called the middle, 
term, with which each of the others may be com- 
pared in turn. This is mediate inference. If one 
fufpe&s that " this liquid is poifon," it may be im- 
poffible to convert the fufpicion into certainty, until 
one has found that u it contains arfenic 5" " contain- 
ing arfenic" will then be the middle term, which will 
be compared in a judgment with each of the others 
in turn ; and the whole argument will run, cc This 
liquid contains arfenic ; and every thing that contains 
arfenic is poifonous ; confequently this liquid is." 
We will fay nothing at prefent of the means of find- 
ing middle terms, although, as in the given example, 
long trains of thought or patient obfervation may be 
required to fecure them. 

But fometimes, inftead of a third term, differing 
entirely from the other two, the premifs only need 
contain the two terms of the conclufion, or fome 
modification of them. Thus from " All good rulers 
are juft" we infer that "No unjuft rulers can be 
good," a judgment introducing indeed no new mat- 
ter, u e. making us acquainted with no new facts ; 
but ftill diftinct from that from which we drew it, as 

o 



194 OUTLINE OF THE 

reprefenting the matter under a new form. Here, 
for purpofes of inference, there are not three different 
terms, becaufe jujl and unjuji^ though they ftand for 
two feparate fets of objefts, have a particular rela- 
tion, each implying the exiftence of the other. # 
Some Logicians refufe the name of inference to this 
and fimilar proceffes, on the ground that " there is 
in the conclufion no new truth, nothing but what 
was already afferted in the premiffes, and obvious to 
whoever apprehends them."f That the conclufion 
is virtually afferted in the premiffes, is true not only 
of thefe immediate inferences, but of all fyllogifms 
whatever; even in the indu£Hve, the mere con- 
fequence — the a£t of concluding — brings in nothing 
which is not known potentially as foon as we have 
the whole grounds before us. So that the obje&ion 
proves too much ; as it would difqualify a fet of in- 
ferences which no one thinks of rejecting. If how- 
ever there is abfolutely nothing new — if the concef- 
fion of the premifs is not only a virtual, but an ac- 
tual and exprefs declaration of the conclufion, there 
is no inference, but mere repetition. But who can 
fay that " No unjuft rulers are good" is a bare repe- 
tition of" All good rulers are juft ?" In the one we 
affirm, in the other deny; in the one the fubje£t of 

* See § 61. f Mill's Logic, B. a. ch. i, 2. 



LAWS OF THOUGHT. 195 

thought is " good rulers," in the other " unjuft 
rulers/' They are, in thefe two points at leaft, dif- 
tincT: judgments, and as the paffing of the one makes 
it poffible without further obfervation or decifion 
upon facts, to collect the other, there is an inference. 
In many fuch cafes, it is true, the inference is fo ob- 
vious, fo certain to occur upon the firft glance at the 
premifs, that it feems needlefs to draw it out ; but 
all the inferences we are about to fpecify are ufed 
from time to time, and this entitles them to our con- 
fideration. 

The fame objection would lie againft all attempts 
to give rules for the immediate inferences, as would 
be brought againft a definition of the colour blue, or 
fcientific directions for walking; namely, that the 
things themfelves are fo fimple that we underftand 
them perfectly without directions. It is eafier to dis- 
cover for ourfelves the principle of any cafe that may 
arife, than to charge the memory with a lift of all the 
cafes and their laws ; and therefore few ftudents will 
go beyond the fimple examination of the following 
fections, which are neceffary to the completenefs of 
our analyfis of thinking. 

§ 84. Oppofttion and Inferences depending on it. 

Oppofition of judgments is the relation between 
any two which have the fame matter, but a different 



196 OUTLINE OF THE 

form, the fame fubje£i and predicate, but a different 
quantity, quality, or relation. Between " No form 
of government is exempt from change," and " Some 
forms of government are exempt from change," 
there is an oppofition, called by logicians contradic- 
tory, the rule of which is that one or other of the 
judgments muft be true, that no intermediate one is 
poffible, and that both cannot be true together. 
Hence it refults, that if I lay down that " No A is 
B," I imply the impoffibility of laying down " Some 
A is B," or in technical phrafeology, if I pofit the 
one I remove the other. And again, the refufal to 
adopt " No A is B," is equivalent to laying down 
that cc Some A is B ;" the removal of one implies the 
pofition of the other. The do6hine of oppofition 
has to fhow what may be inferred as to the truth or 
falfehood of any other kind of judgment, from the 
truth or falfehood of a given one, the fubject and pre- 
dicate remaining always the fame. Arbitrary names, 
fandtioned by the earlieft ufage, have been given to 
the relation between each pair of judgments, to which 
fome addition has been rendered neceflary by the 
new judgments U and Y. But the terms chofen are 
fuch as convey their own meaning; and where it 
was poffible, the well-known names have been ex- 
tended to new relations, inftead of introducing new 
ones. 



LAWS OF THOUGHT. 



*97 



Tables of Opposition of Judgments. 

I. 

A . . Contrary . . E . . Contrary . . U 



jo 
co 






* 



CO 



V 



6 



c? 



5=1 



Subcontrary . O . Subcontrary . Y 



II. 



Inconfiftent . U 



jo 

CO 



4 



«$> 






I . . . Subaltern . . . Y 

There are five kinds of Oppofition, Contradic- 
tory, Contrary, Inconfiftent, Subaltern, and Sub- 
contrary. 

Contradictory oppofition* is the moft perfect, as 
we can infer both from the pofition of a judgment the 
removal of its contradictory, and from the removal 



* Ariftotle often called judgments of this kind fimply " op- 
pontes" (avTiKslfjizwi), as if he confidered contradictory oppo- 
fition the oppofition par excellence, Waitz, on Org. xi. b. 16. 



198 OUTLINE OF THE 

of the judgment the pofition of its contradictory, as 
has been fhown above. It only exifts between the 
judgments E and I. Other writers defcribe A and O 
as contradictories ; but the fa£t is that we cannot tell 
from the removal of O, whether we ought to replace 
it by A or U. Let the O " Some men are not ra- 
tional animals " be removed, u e. its truth denied, 
and that removal will not eftablifh the A, " All men 
are (fome) rational animals/' A third judgment is 
poffible, namely that w All men are all rational ani- 
mals" — the only rational animals there are, and 
which of thefe two is to apply, cannot be inferred 
from the O, but muft be afcertained from the fails 
of the cafe. 

Contrary oppofition exifts between affirmative and 
negative judgments which cannot be true together, 
but which may be falfe together; that is, between 
A and E, E and U, E and Y, U and O, and A and O. 
From the pofition of a judgment we are able to infer 
the removal of its contrary ; but the judgment may 
be removed or denied, without the pofition of the 
contrary. If it is laid down that " All men have a 
right to freedom," it becomes impoffible to lay down 
that "No men have a right to freedom;" but of 
courfe it does not follow from the refufal to admit 
that "All men have the right," that therefore no 
men have. 



LAWS OF THOUGHT. 199 

Inconfiftent oppofition lies between any two af- 
firmative judgments which cannot be correct toge- 
ther, but may be falfe together; that is, between A 
and U, U and Y, and A and Y. Here it becomes 
neceffary to attain a more precife notion of the dif- 
ference between A and U. Suppofe the example of 
U to be " Animals are things endowed with life and 
fenfation $" which means — that "animals" and 
" things endowed with life and fenfation" are but 
two modes of reprefenting the fame thing, and are 
therefore interchangeable. Let the example of A be 
" All men are animals ;" — can we fay that this judg- 
ment has the fame properties as the other ? can we 
put "animals" wherever "men" mould come into 
our thoughts ? No ; " animals" is a very wide clafs, 
containing "men" and a vaft number of other fpe- 
cies. We mean by our judgment, not that men and 
animals are juft the fame things, but that men are 
contained in the wider clafs animals. This relation 
might be reprefented to us by making " men" a fmall 
circle, within " animals" a large one ; whilft the re- 
lation between fubjecT: and predicate in U would be 
beft conceived as that of two equal circles laid one 
upon the other. Now every judgment which is 
really A, and not U, /. e. which really has an undis- 
tributed predicate, means that the predicate is wider 
than, and contains, the fubjedt; whereas every U 



200 OUTLINE OF THE 

means as certainly that the predicate is no wider than 
the fubjeft. It is true that we fometimes form an A 
where we might form a U ; as in faying that " All 
men are (fome ) rational animals," from a belief that 
in a higher ftate of being, or in another planet, there 
may be rational animals to whom it would be im- 
proper, from their other charafteriftics, to apply the 
name of men ; where another, difbelieving the ex- 
iftence of any creatures befides men, to whom the 
name could apply, may hold that " All men are all 
rational animals." But this does not make the judg- 
ments true together. Which is true depends upon 
the fafts ; and the reafon that two perfons hold the 
two judgments together, or one perfon holds them at 
different times, is that they know the fa£ts with dif- 
ferent degrees of corre£tnefs. Where the facSs 
judged upon are fairly and fully known, an A and U 
can never reprefent them with equal correftnefs, nor 
can ever be true together. They are inconfiftent. 

Subaltern oppofition is between any pair of affirm- 
ative or negative judgments, when the one has fewer 
terms diftributed, that is, taken entire, than the other. 
That in which there is more diftribution is called 
the fubalternant, and that which has lefs or none, the 
fubalternate ; or they may be termed the higher and 
lower. The inference here is that when the higher 
is laid down the lower follows ; but nothing follows 



LAWS OF THOUGHT. 201 

from denying the higher, or laying down the lower. 
I is the fubalternate to A, O to E, I to U, and I to 
Y ; fo that from any A, U or Y follows an I, and 
from any E, an O. The name of oppofition lefs 
properly applies here, as the relation of the judg- 
ments is really a partial agreement. 

Subcontrary oppofition is between particular judg- 
ments, of which one is affirmative and the other ne- 
gative, viz. I and O, O and Y. The name fubcon- 
trary is altogether arbitrary and without meaning, as 
the judgments have no real contrariety, but rather a 
prefumption of agreement. They are oppofed, ac- 
cording to Ariftotle, only in the form of expreffion.* 
If " Some men are wife" be the whole truth, u Some 
men are not wife," its fubcontrary, follows of courfe; 
and it has been ingenioufly remarked by Tcletus, 
that in this kind of oppofition there is not the fame 
fubjeft in the two judgments, for we mean in one 
" Some men" and in the other " Some other men." 
Each pair of judgments may be true together; and I 
and O cannot be falfe together. The oppofition of 
Y and O, though we have not given it a feparate 
name, has thefe peculiar properties, that if Y be true, 
O muft be; and that they maybe falfe together. To 



* An. Pri. II. 15. Ammonius terms them vffEvavrlag, and 
Boethius fubcontr arias . 



202 OUTLINE OF THE 

diftinguifh it, we may call it y# ^-contrary oppofition. 
Two judgments # cannot be called oppofites 5 un- 
lefs the fame fuhjedt be joined with the fame predi- 
cate at the fame time, and under the fame circum- 
ftances in both. " The Englifh are very rich," and 
" The Englifh are not very rich," may be true to- 
gether, if Englifh capitallfts are referred to in the 
former, and the public revenue of England in the 
latter. Moreover, if the judgment imply an aft of 
comparifon with fome third thing as a ftandard, the 
fame ftandard muft be preferved in its oppofite. It 
is not uncommon to hear two fuch judgments as 
" This houfe is very large" and " This houfe is very 
fmall," pronounced by two people who are com- 
paring it with two different ftandards, the one per- 
haps with his own little cottage, the other with 
Blenheim or Stowe. But thefe rules refolve them- 
felves into one — we muft be perfectly fure,by dif- 
tinftly underftanding the fubjeft and predicate, that 
they are in all refpe£ts the fame in both judgments. 

§ 85. Converfion of judgments ^ and Inferences 
from it. 

Converfion is the tranfpofition of the fubjeft and 

* Ariftotle, de Interp. ch. vi. § 5. The Latin logicians fay- 
that in both judgments we muftfpeak de eodem fecundum idem, 
ad idem, eodem mo do, eodem tempore. 



LAWS OF THOUGHT. 203 

predicate of a judgment, to form a new one. The 
judgment to be converted is called the convertend, 
and the new one which refults from the tranfpofition, 
the converfe. By converfion, for example, "♦ Some 
falts are fufible," would become " Some fufible fub- 
ftances are falts." The converfe, as having a differ- 
ent fubjecl: of thought (p. 144) from the convertend, 
is a new judgment, not merely a different ftatement 
of the convertend ; for it cannot be the fame to think 
of " falts" and afcertain what can be attributed to 
them, as it is to think of " fufible fubftances," and 
afcertain what is to be predicated of them. And 
as the converfe depends entirely for its truth upon 
the convertend, we muft regard it as an inference 
from it. 

In right converfion, the quality of the judgment 
is preferved, and each term that was diftributed is 
diftributed in the converfe, but no other. Hence we 
cannot infer from u Some fceptics are vicious " that 
u All vicious perfons are fceptics ;" we fhould diftri- 
bute the term "vicious perfons/' where the premifs 
exhibited it undiftributed. Remembering this rule, 
we may difpenfe with the common divifion into fim- 
ple,* and accidental, converfion. The fix kinds of 

* Simple converfion is where the converfe is of the fame 
Quantity as the Convertend 5 converfion per accidens where 



2o 4 OUTLINE OF THE 

judgments give the following converfes refpeftively, 

A is converted to Y 

E E 

I ..... I 

O n 

U U 

Y A 

Upon the converfion of A it may be remarked, that 
fince any judgment and its converfe are but two 
forms of the fame matter^ i. e. two modes of think- 
ing upon the fame fairs, we ought to be able to re- 
cover by re-converfion the fame judgment weat firft 
converted, otherwife, if we are obliged to reft con- 

the rule of diftribution given above, obliges us to make a par- 
ticular converfe from a univerfal proportion. Ariftotle ufes 
the words Kara avfA0e0rutog (per accidens) to exprefs " with lefs 
propriety — improperly/' where a thing happens to have a 
name given to it to which it has no natural (nark <pv<riv) title. 
Boethius applied the name Accidental to an irregular conver- 
fion, where from our knowledge of the matter we bring out a 
converfe not formally prefent, as in converting the conclufion of 
Bramantip in the common books. Thence later writers apply 
the name to what Ariftotle has called " particular converfion. " 
Simple Converfion is fo called properly and naturally, becaufe 
the proportion fuffers no other change than a tranfpofition of 
terms. But Converfion per accidens is called converfion " lefs 
properly," becaufe the proportion which was univerfal before 
is now particular, fo that there is fomething more than mere 
converfion. Berlin Scholia 175, a. 27.5 Wait% on Org. 43, a. 
34 j Sir W. Hamilton, in Mr, Baynes'' Analytic, p. 28, note. 



LAV/S OF THOUGHT. 205 

tented with a weaker form, we find that our know- 
ledge of the fa£ts is lefs now than when we began to 
convert. By the common rules, A is to be con- 
verted to I, and that can only be reconverted to I. 

The judgment O is ufually confidered inconver- 
tible by the ordinary method. But unlefs we regard 
the effential difference of fubje£t and predicate, it is 
hard to fee the reafon. Unqueftionably in fuch a 
judgment as " Some fubftances do not tranfmit light," 
there are two terms, the diftribution of which we 
know; why then may we not tranfpofe them, into 
" No things which tranfmit light are fome fub- 
ftances ?" Becaufe every judgment mould exprefs 
fome new truth concerning its fubjeft, which this 
converfe appears not to do. The former judgment 
might be the refult of experiments, and contains 
fubftantial information, namely that there are fub- 
ftances not permeable by light. But it is ufelefs to 
know that no things which tranfmit light are fome 
fubftances, for after all they may be fome other fub- 
ftances. We ought to treat O then as inconvertible, 
becaufe its converfion feems to be fruitlefs. 

§ 86. Immediate Inference by means of Privative 
Conceptions, 

Every conception, we have (qqu^ has a correfpond- 
ing conception called a privative. The pofitive con- 



206 OUTLINE OF THE 

ception has marks, but all we know of the privative 
is that thofe marks are wanting to it. " Unwife," a 
privative conception, includes whatever " wife," the 
pofitive, does not. Now it is impoffible to pafs any 
judgment upon a pofitive conception, without imply- 
ing others upon the privative ; and hence arife many 
immediate inferences. They are here fubmitted in 
a tabular form,* not of courfe to be committed to 
memory, but to be carefully examined, as a prepara- 
tion for the practice of fupplying fimilar ones to any 
judgments that occur — an exercife favourable to 
acutenefs, and readinefs in interchanging equivalent 
ftatements. In the examples, privative words with 
the prefixed fyllable un or in have been employed, 
to avoid a multitude of puzzling negative particles. 
In each group of three judgments, the firft is the 

* ProfefTor De Morgan has furnifhed the pattern for this 
Table in his "Formal Logic," p. 61 5 the additions I have 
made are fuch as the two additional judgments U and Y made 
indifpenfable. No earlier writer has taken the trouble to draw 
out fo carefully and clearly the various judgments in which 
privatives may be employed. The common books ufe it in two 
cafes, of which thefe are examples ; " All animals feel/' then 
" Nothing which does not feel can be an animal :" " Some 
judges are not juft," then " Some not-juft perfons are judges." 
Ariftotle omits it. Leibniz, (Op.xx.p. 98. Erdmann Ed.) indi- 
cates that there are many forms of privative predication, but 
does not purfue the fubjecl:. 



LAWS OF THOUGHT. 207 

premifs, and the other two are inferences from it ; 
and in the firft divifion the premifs of each group 
contains pofitive conceptions ; in the fecond, priva- 
tive. 

Division I. 

A. All the righteous are happy ; 

Therefore, None of the righteous are unhappy j 
And, All who are unhappy are unrighteous. 

E. No human virtues are perfect j 

Therefore, All human virtues are imperfect 5 
And, All perfect virtues are not human. 

I. Some poflible cafes are probable ; 

Therefore, Some poflible cafes are not improbable ; 
And, Some probable cafes are not impoflible. 

O. Some poflible cafes are not probable 5 

Therefore, Some poflible cafes are improbable ; 
And, Some improbable cafes are not impoflible. 

U. The juft are [all] the holy 5 

Therefore, All unholy men are unjuft 5 
And, No jufl men are unholy. 

Y. Some happy perfons are [all] the righteous ; 

Therefore, All who are unrighteous are unhappy $ 
And, No righteous perfons are unhappy. 

Division II. 

A. All the infincere are difhoneft ; 

Therefore, No infincere man is honeft 5 
And, All honeft men are fincere. 

E. No unjuft act is unpunifhed ; 

Therefore, All unjuft acts are punifhed 5 
And, All acts not punifhed are juft. 



208 OUTLINE OF THE 

I. Some unfair acts are unknown 5 

Therefore, Some unfair acts are not known 5 
And, Some unknown acts are not fair. 

O. Some improbable cafes are not impoffible 5 

Therefore, Some improbable cafes are poflible 5 
And, Some poflible cafes are not probable. 

U. The unlawful is the [only] inexpedient 5 
Therefore, The lawful is the expedient 5 
And, the lawful is not the inexpedient. 

Y. Some unhappy men are all the unrighteous ; 
Therefore, No happy men are unrighteous 5 
And, Some unhappy men are not righteous. 

Let it be remarked that the fubftantives we infert 
into thefe judgments prove that we do not divide the 
whole univerfe into happy and unhappy, jufl: and un- 
juft, &c. but fome more limited clafs of exiftences, 
fuch as cafes ) acls^ perfons (p. 120). And as to the 
ufe of fuch inferences as thefe, it may be noticed that 
men frequently throw a judgment into one of thefe 
inferential forms, before they can determine upon its 
acceptance or rejection. It would be natural, upon 
being allured that u All the righteous are happy," to 
exclaim — u What ? Are all the unhappy perfons we 
fee then to be thought unrighteous ?" Among the 
above inferences there are no mere converiions, fo 
that from any premifs its converfe may be inferred 
befides. 



LAWS OF THOUGHT. 209 

§ 87. Immediate Inference by added Determinants. 

Some mark may be added to the fubjeft and pre- 
dicate, which narrows the extent of both, but renders 
them more definite^ — better determined (§ 54). And 
from the fimple judgment, we may infer that which 
has the additional mark, provided that the diftribu- 
tion of terms remain unchanged. Thus "A negro 
is a fellow creature, Therefore a negro in fuffering 
is a fellow-creature in fuffering." Even two judg- 
ments* may be amalgamated upon this principle ; 
thus " Honefty deferves reward, and a negro is a 
fellow-creature, Therefore a negro who mows ho- 
nefty is a fellow-creature deferving of reward. 

§ 88. Immediate Inference by Complex Conceptions. 

This inferencef is parallel to the laft ; inftead of 
a new conception added as a mark to fubjeft and 
predicate, the fubjecT: and predicate are added as 
marks to a new conception. For example, u Oxy- 



* See Leibniz, Op. xix. Theor. 3. Si coincidentibus ad- 
dantur coincidentia, fiunt coincidentia. Si A z: B et L = M 
erat A + L — B -f M. See alfo Op. xx. 4. 

f See Leibniz, Op. xix. Theor. 3. "Si eidem addantur 
coincidentia, flunt coincidentia." This valuable paper would 
be much clearer, if the great author had diftinguifhed between 
exteniion and intenfion. 



2io OUTLINE OF THE 

gen is an element, fo that the decompofition of oxygen 
would be the decompofition of an element." Here 
again, the terms muft be diftributed in the conclu- 
fion or not, according to their diftribution in the 
premifs. 

§89. Immediate Inferences of Interpretation. 

It has been fliown already (§ 80) that every judg- 
ment may be interpreted in three different ways, 
according as we regard it from the fide of extenfion, 
or of intenfion or of denomination. Thefe are not 
ftri&ly inferences from the judgment, becaufe when- 
ever it is perfectly underftood, they are parts of it ; 
but relatively to a mind not fully perceiving all that 
the judgment really conveys, they are inferential, 
and we may call them inferences of interpretation. 

Lambert # has given one or two other formulae 
which may come under the fame title. " A is B, 
therefore B exifts" and a A is B, therefore where A 
is we find B." Thefe may be refolved into one, of 
which an example may fhow the ufe. " Howard 
exhibited this high philanthropic fpirit, therefore fuch 
philanthropy really exifts," L e. is not merely imagi- 
nary. We make a tacit diftinftion between our 
notions of real obje£ts and thofe from imagination or 
from grounds that are palpably falfe.f Taking our 

* Neues Org. 1. ch. i. § 259. f See p. 172. 



LAWS OF THOUGHT. 211 

notions of Socrates, Heracles, and the Chimaera, we 
fee that in the cafe of Socrates a conviction is im- 
plied that he is a real perfon, in that of Heracles 
that the reprefentation we have of him is at moft 
only partly real, in that of the Chimaera that it is a 
mere invention of the poets. In all our real notions 
we imply the mark of exiftence, and a negledt of it 
leads invariably to an abfurdity. I cannot call it, 
with M. Duval- Jouve,* a judgment, becaufe it is 
rather the refult of a former judgment ; when we 
think of volcanoes, we do not judge that they exift, 
becaufe we have long fince done fo, and always think 
of them as exiftent. Farther, every attribute of a 
real object is itfelf real ; and therefore when we fay 
that Howard was an exalted philanthropift, we of 
courfe imply that the exiftence of exalted philan- 
thropy is eftablifhed by the fa£t of Howard's ex- 
iftence. But where doubts were entertained that our 
ideal of philanthropy had ever been realized, the ex- 
ample before us would have place. 

* Logique. §13. A\fo Damiron, Logique p. 12, who 
regards judgment as the termination of all the acls of the 
underftanding, whereas in the prefent work it is treated as 
preparatory to conception, as undertaken for the fake of more 
precife and complete notions. But of courfe an " exiftential 
judgment" maybe formed, as any other analytic judgment 
may, with any real conception as the fubjecl ; " Man exifts, 
the world exifts." Compare Reid, Effay vi. ch. 1, p. 4.13, of 
Sir W. Hamilton's Edition. 



2i2 OUTLINE OF THE 

§ go. Immediate Inference from a Disjunclive 
Judgment. 

A disjunctive judgment exprefles an act of Divi- 
fion, as " The teeth are either incifors, canine, bi- 
cufpid or molar teeth." According to the rule of 
mutual exclufion of the dividing members (§ 57) we 
might infer from the judgment juft given, that "The 
molar teeth are neither incifors, canine, nor bicuf- 
pid." According to another rule, that the members 
muft completely exhauft the divifum, we infer that 
the part of the divifum not contained in one member, 
muft be in fome other. " All teeth which are not 
molar, are either canine, incifors, or bicufpid teeth." 

Formula I. 

All AisX YorZ; 
Therefore the X of A is not the Y or Z of A. 

Formula II. 

All A is X Y or Z 5 
Therefore the not-X of A is the Y or Z of A. 

§ 91. Immediate Inference by the Sum of fever al 
Predicates. 

After examination of the properties of any fubject, 
it is neceflary to collect: the various predicates which 
have been affigned it, in order to combine them for 



LAWS OF THOUGHT. 213 

a definition. The definition of copper, for example, 
that it is " a metal— of a red colour — and difagreeable 
fmell — and tafte — all the preparations of which are 
poifonous — which is highly malleable — du£tile — and 
tenacious — with a fpecific gravity of about 8*83," is 
the refult of as many different prior judgments as 
there are properties affigned. From a fufficient num- 
ber of judgments in A, having the fame fubjeft, a 
judgment in U may be inferred, whofe predicate is 
the fum of all the other predicates. 

§ 92. Concluding Remark. 

Whilft it is at once admitted that thefe immediate 
inferences — fyllogifms of the underftanding as they 
are called by Kant, to diftinguifh them from the me- 
diate fyllogifm of reafon — are obvious enough when 
they appear fingly, the great number and variety of 
them, may be thought a fufficient reafon for examin- 
ing them. Could any perfon not accuftomed to ex- 
ercifes of this kind, draw out fully all his own mean- 
ing, when he utters the fimpleft propofition ? The 
judgment "All men are mortal," (a plainer cannot 
be found) tells us — that man is one fpecies in the clafs 
of mortal beings — that the mark of mortality mould 
always accompany our notion of man — that the word 
mortal is a name which may rightly be given to 
man — that, if all are mortal, any one man is — that 



214 OUTLINE OF THE 

any ftatement which affirms that no men are mortal 
muft be quite falfe — that even the ftatement that 
fome men are not mortal is equally falfe — that fince 
man is contained in the clafs of mortal things, which 
is a wider clafs, it would be wrong to fay all mortal 
things are men — that, however, the affertion " Some 
mortals are men" would be true enough — even 
" Some mortals are all men"— that no men can be 
immortal — that any immortal beings muft be other 
than men — that mortality really exifts, being found 
in man, whom we know to exift — that a man with 
immortal hopes is a mortal with immortal hopes — 
that (fince heaven is immortality) a man expecting 
heaven is a mortal looking for immortality — that he 
who honours a man, honours a mortal. Thus from 
this fimple judgment fourteen judgments have un- 
folded themfelves, or, as fome would fay, the judg- 
ment has been put in fifteen different ways, in the 
laft three of which only is any new matter introduced. 
And yet any man of common fenfe would fay that 
his propofition really implied them. 

§ 93. General Canon of Mediate Inference, 

The law upon which all mediate inference de- 
pends may be thus exprefTed. The agreement or dif- 
agreement of one conception with another^ is afcertained 
by a third conception^ inafmuch as this^ wholly or by 



LAWS OF THOUGHT. 215 

the fame part^ agrees with both^ or with only one of 
the conceptions to be compared. The mediate fyllo- 
gifm, or (as it is ufually called) the fyllogifm, is a 
comparifon of any two notions with a third, in order 
to afcertain whether they agree or not. Suppofe the 
queftion is whether this difeafe is mortal ; in order to 
afcertain the agreement of the two notions, fo that 
we may fay " This difeafe is mortal," we find a third 
notion, that it is a confumption, which we know to 
be mortal, and then the whole fyllogifm will be 

All confumptions are mortal, 
This difeafe is a confumption ; 
Therefore it is mortal. 

All the properties of a fyllogifm depend upon the 
Canon juft laid down ; as will be feen when they are 
enumerated. 

1. A fyllogifm will contain three notions and no 
more, namely, the two whofe agreement or difagree- 
ment we flrive to afcertain, and the third which we 
employ as a means of doing fo. They are called 
terms ; and the third notion, interpofed between the 
others in order to compare them, is the middle term, 
whilft the other two may be called, from their place 
in the concluding judgment of the fyllogifm, the fub- 
jecl and predicate. 

Formerly, the fubjedt. of the conclufion was called 
the minor term, and the predicate the major^ becaufe 



216 OUTLINE OF THE 

in one form of inference, fuppofed to be the moft 
perfect, the major was by its pofition moft extenfive, 
and the minor leaft; thus, in the fyllogifm "All 
men are mortal, Socrates is a man, therefore Socrates 
is mortal 5 ' — -mortal, the major term, is more exten- 
five than Socrates, the minor ; for, in mortal we in- 
clude Socrates and all other men. But in negative 
inference it is impoffible to afcertain the comparative 
extent of the terms. If the conclufion were " No 4 
beafts of prey are ruminant," it would be impoffible 
to afcertain which term were the more extenfive, — 
whether " beafts of prey" applied to more objects 
than ruminant— inafmuch as the judgment itfelf de- 
clares that they have nothing to do with one ano- 
ther, and one cannot therefore be applied to meafure 
the other. The fo-called major term might happen 
to be a good deal lefs than the minor. When the 
concluding judgment is particular, the fame abfurdity 
attaches to the names. In " Some brave men are 
prudent" it is impoffible to fay whether " brave men" 
or " prudent men" is the more extenfive term. The 
names of major and minor then are only defcriptive, 
when applied to fome particular forms of fyllogifm. 
But they are fo interwoven with logical phrafeology, 
that it will be better occafionally to annex them in a 
parenthefis to the lefs objectionable ones. 

2. A fyllogifm mujl contain three judgments and no 



LAWS OF THOUGHT. 217 

more. Since it contains three terms, each of which 
is to be compared, once only, with every other, there 
would be three acts of comparifon, each expreffed 
by a judgment. Three terms cannot be joined in 
more than three pairs without repetition. 

The two judgments in which the middle term 
occurs, are called the premifTes, and the remaining 
one the conclufion. That premifs in which the pre- 
dicate (major term) is compared with the middle, 
was formerly called the Major premifs, and the other, 
in which the fubjeft (minor term) occurs, was the 
Minor premifs. The former was alfo fometimes 
called the Propofition, and the latter the Aflump- 
tion, and fometimes the Subfumption. But all thefe 
names are inconfiftent with the wider view of in- 
ference now taken ; and it will be fufficient to call 
the premifTes firjl and fecond^ the firft being always 
that in which the predicate of the conclufion occurs, 
whether it ftands firft in order or not. 

3. One premifs at leaft muft be affirmative. The 
Canon provides that one term at leaft muft agree with 
the middle, that is, muft be united with it in an affir- 
mative judgment ; and without this, there can be no 
inference about the two terms which are to be com- 
pared. With the premifTes " No ram man can be 
a good general, and Xenophon was not a rafh man," 
we could neither have the conclufion that Xenophon 



218 OUTLINE OF THE 

was a good general, nor that he was not. The pre- 
miffes afford no data for difcovering in what fort of 
judgment the terms Xenophon and good general 
may come together. 

4. The worft relation of the two terms with a 
third, thai may be ejiablijhed in the premiffes, Jhall 
be expreffed in the conclufion. Now the beft and moft 
intimate relation of two terms is that of abfolute 
identity of matter, as in " An animal is a being with 
life and fenfation ;" the next exifts where the whole 
of one term coincides with part only of the other, 
as in " All organized ftruftures decay ;" the loweft 
relation, where part of one term coincides with part 
of another, as in cc Some flowers are blue." If the 
two premiffes exprefs two different relations, the con- 
clufion muft follow the inferior. Thus "All tri- 
angles = figures with three fides, A B C is a (fome) 
triangle, Therefore A B C is a (fome) figure with three 
fides :" where the chief-predicate though diftributed 
in the premifs is not in the conclufion. The worft 
pofitive relation then which the premiffes contain, is 
all that can be inferred in the conclufion. 

5. On a fimilar principle, if one of the premiffes 
be negative, the conclufion muji alfo be negative. The 
Canon only fuppofes two conditions, under one of 
which an inference muft be made ; that of agree- 
ment of two terms with a third, expreffed by affirma- 



LAWS OF THOUGHT. 219 

tive premiffes, and confequent agreement of the two 
terms, expreffed by an affirmative conclufion ; and 
that of agreement of one term and difagreement of 
another, with the third term, expreffed in an affirma- 
tive and a negative premifs, and confequent difagree- 
ment of the two terms, expreffed in a negative con- 
clufion. The latter condition obtains wherever there 
is a negative premifs, and therefore the conclufion 
will alfo be negative. 

6. The comparifon of each of the two terms muji 
be either with the whole, or with the fame part, of 
the third term. And to fecure this (i) either the 
middle term muft be diftributed in one premifs at 
leaft, or (ii) the two terms muft be compared with 
the fame fpecified part of the middle, or (iii) in the 
two premiffes taken together the middle muft be dif- 
tributed and fomething more, though not diftributed 
in either fingly. 

The wife are good, 

Some ignorant people are good ; 

Therefore fome ignorant people are wife. 

This is only a fyllogifm in appearance, for the two 
terms have only been compared with part of the 
third term good ; if the wife are fome good people, 
and fome of the ignorant zxefome other good people, 
we have compared with two different parts of a 



220 OUTLINE OF THE 

term, which is the fame as ufing two different terms 
— a condition not contemplated by the Canon, and 
one under which there can be no inference what- 
ever. But in the next example (i) the two terms 
meet upon common ground in the third term, be- 
caufe the whole of it is once introduced. 

All the mineral acids are poifons, 
Spirit of fait is a mineral acid 5 
Therefore it is a poifon. 

Here, to whatever portion of the clafs of "mineral 
acids" we refer " fpirit of fait," it muft be a poifon, 
becaufe the whole clafs of mineral acids was brought 
in as poifonous, fo the inference is good. If the firft 
premifs were " half the mineral acids are poifons" 
there would be no inference, becaufe the " fpirit of 
fait" might be in the other half. There would be 
a comparifon with two different parts only of a third 
term. 

The next example (ii) fecures a comparifon with 
the fame part of a third term, not indeed by bringing 
in every part of it, but by fpecifying which part is 
intended in both premiffes alike. 

Certain fciences are claffificatory, 

Thefe fciences = Mineralogy, Botany and Zoology; 

Therefore Mineralogy, Botany and Zoology are claflificatory. 

The fame part of the term fciences being ufed, 



LAWS OF THOUGHT. 221 

the other two terms muft agree. But it is more 
correct to regard " certain fciences" as the whole of 
a fmaller term (§ 76), than as the part of a larger, 
fciences in general. The word " certain," marks it 
off fo definitely that we may confider it a diftincT: 
conception. 

In the next example (iii), that unufual mode of 
diftribution is feen, which is gathered from the two 
premifles combined, although neither contains it fe~ 
parately. 

Three-fourths of the army were Pruflians, 
Three-fourths of the army were flaughtered ; 
Therefore fome who were flaughtered were Pruflians. 

For, even fuppofing that the whole of that fourth 
that were not Pruflians, but (fay) Auftrians, were 
flaughtered, there ftill remain two fourths, mentioned 
in the fecond premifs as flaughtered, who muft have 
been Pruflians. And this kind of inference may be 
drawn wherever the mode of expreflion fatisfies us 
that fomething more than all the middle term has been 
mentioned in the premifles ; the extent of the agree- 
ment between the terms of the conclufion being ex- 
actly meafured by the excefs, over and above the 
whole of the middle term. Thus, cc three-fourths 
of the army," taken twice, make fix-fourths, fo that 
the terms of the conclufion agree to the extent of 



222 OUTLINE OF THE 

two-fourths at leaft of the middle term. Let thefe 
three lines reprefent the terms. 

Pruflians , 

Army « 1 1 1 1 



Men flaughtered 



It appears that the middle line, for two-fourths of 
its length, runs parallel with both the others, and ror 
that diftance, therefore, they run along with each 
other. 

7. Neither term of the conclufion muji be dijiributed, 
unlefs it has been fo in its premifs. For, the refult of 
the comparifon as ftated in the conclufion muft not 
be greater than the comparifon itfelf as made in the 
premifles ; if therefore all of a term appears in the 
conclufion as agreeing with another, a comparifon of 
all of it with the middle muft have been made in the 
premifles. 

Such an inference as 

Pittacus is good, 

Pittacus is wife 5 

Therefore all wife men are good, 

is faulty, becaufe the premifl*es do not contain " all 
wife men." 

Thefe feven general rules of fyllogifm are not new 
principles, to be ftudied as the complement of the 
Canon. They are dire£tly evolved from it, and are 
only fo many cautions to employ it properly. The 



LAWS OF THOUGHT. 223 

Rule of Syilogifm is one and one only, but its confe- 
quences are various, and they are developed in the 
general rules.* 

§ 94. Order of the PremiJJes and Conclufion. 

Although an invariable order for the two premifles 
and conclufion, namely, that the premifs containing 
the predicate of the conclufion is firft, and the con- 
clufion laft,is accepted by logicians, it muft be regarded 
as quite arbitrary. The pofition of the conclufion 
may lead to the falfe notion that it never occurs to us 
till after the full ftatement of the premifles ; whereas 
in the fhape of the problem or queftion it generally 
precedes them, and is the caufe of their being drawn 
up. In this point the Hindu Syilogifm (fee p. 4) is 
more philofophic than that which we commonly ufe. 
The premifles themfelves would afliime a different 
order according to the occafion. It is as natural to 
begin with the fa£t and go on to the law, as it is to 
lay down the law and then mention the fa£t. " I 
have an offer of a commiffion ; now to bear a com- 
miffion and ferve in war is (or is not) againft the 

* They may be remembered by the following hexameters. 
Diftribuas medium, nee quartus terminus adfit, 
Utraque nee praemirTa negans [nee particularis] 
Secletur partem conclufio deteriorem, 
Et non diftribuat, nil! cum praemirTa, negetve. 



224 OUTLINE OF THE 

divine law ; therefore I am offered what it would (or 
would not) be againft the divine law to accept." 
This is an order of reafoning employed every day, 
although it is the reverfe of the technical ; and we 
cannot call it forced or unnatural. The two kinds 
of forites, to be defcribed below, are founded upon 
two different orders of the premiffes ; the one going 
from the narrower!: and moft intenfive ftatement up 
to the wideft, and the other from the wideft and 
moft extenfive to the narroweft. The technical order 
cannot even plead the faniiion of invariable practice.* 
Neither the fchool of logicians who defend it, nor 
thofe who affail it, take a comprehenfive view of the 
nature of inference. Both orders are right, becaufe 
both are required at different times. The one is 
analytic, the other, fynthetic ; the one, moft fuitable 
to enquiry, and the other to teaching. 

* " In confirmation of the do6lrine that the common order 
of the premiffes mould be reverfed, may be added, what not 
one of its modern advocates feems to be aware of, that this, in- 
ftead of being a novel paradox, is an old, and until a compara- 
tively recent period, an all but univerfal practice. It is not 
even oppofed by Ariftotle. For to fay nothing of certain 
fpecial recognitions by him of the legitimacy of this order, his 
ufual mode of ftating the fyliogifm in an abftracl: or fcientific 
form, affords no countenance to the prior pofition, in vulgar 
language of what logicians call the major proposition. Ariftotle 
is therefore to be placed apart. But in regard to the other an- 
cient logicians, who caff their fyllogifms in ordinary language, 



LAWS OF THOUGHT. 225 

§ 95. The Three Figures. 

Every fyllogifm is faid to be in one of three figures ^ 
according to the pofition of the middle term in the 
premhTes. This may be the fubjecl: of the firft pre- 
mifs (major) and the predicate of the fecond (minor), 
in which cafe we fay that the fyllogifm is of the Firft 
Figure : or it may be the predicate of both, which 
constitutes a fyllogifm of the Second Figure : or the 
fubje£t of both, which gives the Third Figure. Thus, 



I. 


11. 


in. 


M P 


P M 


M P 


S M 


S M 


M S 


S P 


.\ S P 


.-. S P 



It has been ufual to call the firft figure the moft 
perfect, becaufe it exemplifies moft directly a certain 



I am able to ftate as follows ; and this in dire£t contradiction 
not only of the implicit afliimptions of our later logicians^ but 
of the explicit afTertions of fome of the moft learned fcholars of 
modern times 5 that the Greeks (Pagan and Chriftian, Peripa- 
tetic, Academic, Stoic, Epicurean and Sceptic) down to the 
taking of Conftantinople, with very few exceptions, placed firft 
in fyliogiftic order what is called the minor propofition. The 
fame was done by the Arabian and Hebrew logicians." [I 
may add the Hindu Gotama to thefe authorities.] " As to 
the Latins they, previous to the fixth century, were in unifon 
with the Greeks. To the authority and example of Boethius 
I afcribe the change in logical pra£Kce. He was followed by 
the Schoolmen, and from them the cuftom has defcended to 
us." Sir William Hamilton. 



226 OUTLINE OF THE 

law of fyllogifm called the diffum de omni et nullo. 
The law is to this effe£t* — " Whatever is affirmed 
or denied of a clafs, may be affirmed or denied of any 
part of that clafs ; " fo that if one affirms of plants 
that they require light, one may affirm it alfo of fun- 
flowers, as a part of the clafs of plants. This would 
require three judgments, one to ftate what we meant 
to affirm of the clafs — " All plants need light 5" — 
a fecond to mention fomething as part of the clafs, 
" Sunflowers are plants ;" and a third to affirm the 
fame of the part as had been affirmed in the outfet of 
the whole ; " Sunflowers require light." Thefe three 
judgments, it will be found, have their terms arranged 
according to the firfl: figure. And on the afliimption 
that the diSfum de omni et nullo was the paramount 
law for all perfe£t inference, and therefore the firfl: 
figure was alone perfe£l,t rules have always been 



* Ariftotle, Cat. ch. 5. Kant puts it Not a not a eft not a ret 
ipftus, viewing the intention of the judgments. Leibniz, Con- 
tentum contenti eft contentum continentis, viewing (I think) their 
extenfion. Leib. feemsto employ includere for the Ariftotelian 
vnct,px* lv i the word that refers to the intention of terms 5 but he 
does not fufficiently diftinguifh between the two. 

f Ariftotle, Pri. An. 1. ch. 5 and 6. Kant, in a little Tracl, 
goes over the fame ground, contending that all the figures but 
the firft, require the converfe of one or other of the judgments 
to be inferted, to make them pure and natural a<5ts of reafoning. 
My reafon for difTenting will be given in the text. 



LAWS OF THOUGHT. 227 

given for reducing, as it is termed, every fyllogifm 
in the lefs perfect figures to the firft. This can 
readily be done by changing the order of the terms 
by converfion (§ 85), or, in the few cafes in which 
converfion will not apply, by fubftituting a privative 
for a pofitive judgment, (§ 86), and then converting. 
But the queftion was raifed — is the diSfum the fole 
law of perfect inference ? Is it not fimply an account 
of the procefs of the firft figure, and might not each 
of the other figures have its diftum too ? The dis- 
covery of new difta* put the procefs of reduction 
in a new light. Each of the figures was found to 
have its own functions, and an attempt to bring the 
two laft to the firft figure, only fpoilt them as exam- 
ples of their own rules. Reduction was therefore 
unneceflary. 

* Thefe are not introduced into the text, becaufe they be- 
long to a fyftem of Logic in which no affirmative judgment 
was held to diftribute its predicate, and in which, to comply 
with the general rules of fyllogifm, the fecond figure mull 
always have a negative conclufion, and the third a particular. 
With our prefent enlarged lift of judgments, they would have 
a very partial application. However, to illuftrate the older 
treatifes they are here given. In the ift Fig. the dictum given 
above. The Fig. is ufeful in arguing from a general to a 
fpecific ftatement. For the 2nd Fig. the diSium de di<verfo — 
" if one term is contained in, and another excluded from, a 
third term, they are mutually excluded.'" Ufeful for mowing 
the differences of things, and preventing confufion of diftincl: 



228 OUTLINE OF THE 

We muft not fuppofe that the divifion of fyllogifms 
according to the figures, is a mere ufelefs fubtlety, 
the refult of an arbitrary attempt on the part of logi- 
cians to difplay the middle term in every poffible po- 
fition. For, firft, the premifles we choofe to eftab- 
lifh fome conclufion by, may be judgments to which 
we are fo accuftomed, that it would be unnatural to 
take their converfe inftead, as might be requifite to 
bring them into the firft Figure. It makes fome differ- 
ence whether " Kings can do no wrong " is to be the 
judgment, or the much more awkward form " Some 
perfons who can do no wrong are kings." But, next, 
it did not efcape Ariftotle that the more extenfive of 

conceptions. For the 3rd Fig. the diclum de exemplo — " Two 
terms which contain a common part, partly agree, or if one 
contains a part which the other does not, they partly differ. " 
Ufeful for bringing in examples, and for proving an exception 
to fome univerfal ftatement. Thus, if it were ftated that all 
intellectual culture improved the heart and conduct, it would 
be natural to fay, in this Figure, " Mr. So and So does not ac"l 
as he ought, yet Mr. So and So is a perfon of cultivated mind, 
therefore one perfon at leaft of cultivated mind does not acl as 
he ought." See Keckermann, Logic in. ch. 7, 8, and 9. Alfo 
Lambert, N. Org. 1. iv. § 229. But Mr. Mill is in an error, 
fhared by Buhle (Gefchichte, vi. 543) and Troxler (Logik, ii. 
p. 62), in thinking that Lambert invented thefe diSla. More 
than a century earlier, Keckermann faw that each Figure had 
its own law and its peculiar ufe, and ftated them as accurately, 
if lefs concifely, than Lambert. Keckermann however ignored 
the 4th Figure, and Lamberfs explanation of that may be new. 



LAWS OF THOUGHT. 229 

two terms ought to be the predicate, that the genus 
fhould be predicated of the fpecies. This is the 
natural, though not invariable, order ; and it is wor- 
thy of remark that in negative judgments, where 
from the negation the two terms cannot be fet toge- 
ther to determine their refpe£tive extenfion, if, apart 
from the judgment, we know that the one is a fmall 
and the other a large clafs, the one a clearly deter- 
mined and the other a vague notion, we naturally 
take the fmall and clearly determined conception for 
our fubjeft. Thus it is more natural to fay that 
" The Apoftles are not deceivers" than that " No 
deceivers are Apoftles." So that, if our minds are 
not influenced by fome previous thought to give 
greater prominence to the wider notion, and fo make 
it the fubjecSt, reverfing the primary order, the figure 
of the fyllogifm will be determined by the exten- 
fion of the middle term. If this term is obvioufly 
wider than the other two, the fecond will be the 
natural figure, becaufe there it will be predicated 
of both. If again, it is obvioufly narrower than 
both, the third, in which it can ftand twice as fub- 
je£t, will be the natural figure. Thus, when it was 
defirable to fhow by an example that zeal and ac- 
tivity did not always proceed from felfifti motives, 
the natural courfe would be fome fuch fyllogifm as 
the following. 



230 OUTLINE OF THE 

The Apoftles fought no earthly reward, 
The Apoftles were zealous in their work ; 
. * . Some zealous perfons feek not earthly reward. 

Admitting that where the extenfion of the concep- 
tions is not very different, either of them would ftand 
fubje£t as well as the other, we contend that fince, in 
fome cafes, natural reafon prefcribes the third figure 
or the fecond, and rejefts the firft, the do£trine of 
the diftin&ion of three figures is not a mere arbitrary- 
invention, but a true account of what takes place in 
the mind. 

§ 96. Special Canons of the Figures. 

Although the Canon of Syllogifm applies fuffi- 
ciently to all the figures, it is poffible to modify it fo 
as to comprehend the order of the terms in each 
figure.* 

Canon of the Firft Figure. 

In as far as two notions are related, either both 
pofitively, or, the one pofitively and the other 
negatively, to a third notion, to which the one is 
fubjeit, and the other predicate, they are related 
pofitively or negatively to each other as fubjeft and 
predicate. 



* Thefe are communicated by Sir W. Hamilton. 



LAWS OF THOUGHT. 231 

Canon of the Second Figure. 
In as far as two notions, both fubje£ts, are, either 
each -positively, or, the one pofitively, the other nega- 
tively, related to a common predicate notion, — in fo 
far are thofe notions pofitively or negatively fubjecSr. 
and predicate of each other. 

Canon of the Third Figure. 

In as far as two notions, both predicates, are, 
either each positively, or, the one pofitively and the 
other negatively, related to a common fubjeft notion, 
— in fo far are thofe notions pofitively or negatively 
fubjeft and predicate of each other, 

§ 97. The Fourth Figure. 
Befides the three that have been given already, 
only one other combination of the terms of a fyllo- 
gifm is poflible, namely, where the middle is predi- 
cate of the firft (major) and fubjeft of the fecond 
(minor) premifs. The introduction of this combi- 
nation as a fourth figure, is attributed to Galen on 
the authority of Averroes.* It would fall into this 
form- p M 

M S 
.-. S P 

* The words of Aver roes are Et ex hoc planum, quodfigura 



232 OUTLINE OF THE 

Many logicians have condemned the ufe of this 
figure. It is defcribed as a mere perverfion of the 
firft, in which the proper conclufion does not appear, 
but the converfe of it, gained by immediate infer- 
ence (§ 85). The meaning of this will appear from 
an example (taken from Abp. Whately's Logic). 

What is expedient is conformable to nature, 

What is conformable to nature is not hurtful to fociety, 

What is hurtful to fociety is not expedient. 

Here it is contended that the mind naturally expe&s 
the converfe of the conclufion, — What is expedient 
is not hurtful to fociety, — which would bring it at 
once to a fyllogifm in the firji figure, and that we 
tacitly draw the proper conclufion before paffing on 
to the unnatural one. But whilft it is plain that fuch 
a conclufion from fuch premifles difappoints the ex- 
pectation, we are unwilling to admit that there is 
any interpolation of a judgment, without fome good 



quart a, de qua memlnit Galenus, non eft Jyllogifmus fuper quern 
cadet naturaliter cogitatio. (In 1 Pri. ch. viii. vol. i. p.63.) I 
have infpe&ed the Dialectic of Galen, published for the iirft 
time at Paris in 1 844, by Minoides Mynas, a Greek, from a MS. 
of the eleventh century found in the Eaft 5 and am of opinion 
— that Galen did not adopt the fourth figure, and that an oc- 
cafional tranfpofition of the premifles in the ift figure may have 
led to the erroneous belief that he did. That his modern 
editor confounds the lit and 4th figures is beyond difpute. 



LAWS OF THOUGHT. 233 

reafon, efpecially as Kant fuppofed the fame fort of pro- 
cefs to have place in the fecond and third figures alfo, 
where it is certainly not required. The reafon now 
to be given for difmiffing the fourth figure as really an 
indirect way of ftating the firft, has not, it is believed, 
been pointed out before. The fubjecft and predicate, 
we remarked, are different in order of thought, the 
fubjeit being thought of for itfelf, and the predicate 
for the fubje£t. Now in the firft figure, the fubje£t 
of the conclufion was a fubje£t in the premifles, 
and the predicate was a predicate, fo that the order 
of thought is ftriftly preferved. So to fpeak, we do 
not depofe a # fubje£t, and fet up a predicate in its 
place. No primary thought becomes fecondary nor 
any fecondary primary. 

All M is P 
All S is M 
.-. All S is P 

The conclufion no way difturbs the order of terms 
eftablifhed in the premifles. But in the fecond figure, 
the order is fomewhat difturbed ; the fubjecft of the 
conclufion was indeed a fubje£t in the premifles, but 
the predicate was not a predicate. 

No P is M 
All S is M 
.-. No S is P 



234 OUTLINE OF THE 

This makes the figure one degree lefs natural than 
the firft ; it departs from dire£tnefs in its ufe of the 
predicate (major term). In the third figure the fame 
indire&nefs occurs ; the fubjeit of the conclufion 
was not a fubjeft in its premifs. But in the fourth 
figure the order is wholly inverted, the fubjeft of the 
conclufion had only been a predicate, whilft the pre- 
dicate had been the leading fubjeft in the premifs. 
Againft this the mind rebels ; and we can afcertain 
that the conclufion is only the converfe of the real 
one, by propofing to ourfelves fimilar fets of pre- 
mifles, to which we fliall always find ourfelves fup- 
plying a conclufion fo arranged that the fyllogifm is 
in the firft figure, with the fecond premifs firft. 

§ 98. The unfigured Syllogifm. 
A fyllogifm may be ftated without making the 
terms either fubjefts or predicates \ fo that it belongs 
to no figure. # Thus " fince copperas and fulphate 
of iron are identical, and fulphate of iron and ful- 
phate of copper are not identical, it follows that 
copperas and fulphate of copper are not identical. " 

§99. Modes of Syllogifm. 
The mode of a given fyllogifm is the formal value 
of its three judgments as to their quantity, quality, 
and relation ; and it is exprefied by the three letters 

* Sir W. Hamilton. 



LAWS OF THOUGHT. 235 

that denote them (§ 78). Thefe, with the addition 
of the number of the figure to which it belongs, con- 
vey the whole form of the fyllogifm; thus All. 
Fig. I. is known to mean 

All M is P 
Some S is M 
. • . Some S is P 
The few perfons who take the trouble to analyfe 
the arguments of works they read, by noting thefe 
and like fymbols in the margin, will bear witnefs to 
the attention and exa&nefs which the practice culti- 
vates, and to the not unfrequent detection of fallacies 
by means of it. 

§ IOO. Table of all the Legitimate Modes in all 
Figures. 

The following Table is an index of the modes 
in which a good inference can be drawn.* It is ar- 
ranged according to the order in which the vowels 
occur in the alphabet, fo that, when any mode has 
been omitted, as not available for inference, the eye 
can deteft and fupply it, and the mind examine the 
reafon for its omiffion. 

* It was drawn up by the Author, independently of all af- 
ilftance from living authorities, in 184.1, andpublifhed in 1842, 
precifely as it Hands here. Another Table is given below, 
with fuch additional modes as contain the doubtful negative 
judgments n and a?. 



236 



OUTLINE OF THE 



Fig. 1. 

AAA 



All 


AU A 


AY I 


E A E 


E I O 


E U E 


E Y O 


I U I 


I Y I 


O U O 


YO 


U AA 


U E E 


U I I 


U O 


u u u 


U Y Y 


Y E E 


Y O O 


Y UY 


Y Y Y 



Fig. 11. 



A E E 



A O 
AU 
AY 
E A 
E I 
E U 
E Y 

I U 
I Y 



O 
Y 
Y 
E 
O 
E 
O 

I 
I 



U AA 


U E E 


U I I 


U O O 


uuu 


U Y Y 


YA A 



Y I I 



YU 
Y Y 



A 
I 



Fig. hi. 
A A I 

All 



AU A 


A YA 


E A O 


E I O 


E U E 


EYE 


I A I 


I U I 


O A O 


O UO 


U A Y 


U E E 


U I I 


U O O 


UUU 


U Y A 


YA Y 


YE E 



YU Y 



Some of thefe modes exemplify different fpecial 
rules and theorems of logical writers, of which a 
few are fubjoined. 



u 



o 

u 



u 

u 






o 



u 






P u 









u 



K 









s? 


,4- 


^ 




-»i 


c/; 


« 


6 


<i 


O 






u 


o 




a. 

c 






<v 


p^ 


*n 




o 


u 


£ 


-(-> 




o 


0) 


fi 


43 


^ 


o 


>-, 


43 


c 
o 


h 


00 

P 



pq 



55 






LAWS OF THOUGHT. 237 

Fig. I. AAA and A A I are the only modes to which 
the dittum de omni directly applies — " Whatever is faid of a 
clafs may be faid of a contained part of the clafs." 

Fig. I. A U A is a formula into which a " perfect induc- 
tion " might fall, where we affirm fomething of a whole clafs, 
becaufe we have found it true of all the individuals or fpecies 
which the clafs contains. Thus 

x y and z are P 
S — xy and z 
Therefore S is P 

Leibniz gives the formula " Cui fingula infunt, etiam ex 
ipfis conftitutum ineft." 

Fig. I. E A E and E I O are the only modes to which the 
diSium de nullo applies. " What is denied of a clafs mult be 
denied of any part of the clafs." 

E U E and U E E in all figures. " Si duomm quae funt 
eadem inter fe unum diverfum fit a tertio, etiam alterum ab eo 
erit diverfum." Leibniz. 

Fig. I. and II. U A A. " Quod inert uni coincidentium, 
etiam alteri ineft." Leibniz. 

M = P 

All S is M 
. • . All S is P 

UUUin all figures. " Quae funt eadem uni tertio, eadem 
funt inter fe." 

§ 101. A mode of Notation. 

To be able to reprefent to the eye by figures the 
relation which fubfifts in thought between concep- 
tions, tends fo greatly to facilitate logical analyfis, 
that many attempts have been made to attain it. Of 



SIR WILLIAM HAMILTON'S SCHEME OF NOTATION. 

Fig. i. Fig. ii. Fig. hi. 



ii. C, ■ : M : ,T C, : M : , T C, . : M : ,T 



, C, . : M, :T C, : M , :T C, : M , :T 



iv. C: ■ , M : -,T C: , M : , T C: ■ , M : ,T 



v . C, : M, .,T C, : M, , T C, . : M , ,T 



vi. C, , M : ,T C, , M : ■ ,T C, , M : ,T 

vii. C:- 



M : ,T C:— : M : , T C :• 



M : . ,r 



. c, : M : .-.T C, : M : 



ix. 

X. 

xi. 

- xii 


C: 

C: 
C: 

c, 


. . m, 


r 

,r 


C> 


X 

, M : . 


C: 


: M, 


C: 


X 

, M : 


c, 



-:T C,. 
-:T C: 

-:F C: 



M : i 



M , :T 



: M, ,T C:- 



, , M : :T 



M . 



-:T C,. 



, M 



A. i. and ii. are balanced. B. The other modes are unbalanced. Of thefe, iii. and iv. are unbalanced 
in terms only, not in propofitions ; the reft in both. 



238 OUTLINE OF THE 

two important fchemes, that of Euler and that of 
Sir W. Hamilton, an account will be given hereafter. 
The fcheme now to be explained is that which Lam- 
bert makes ufe of, in his Neues Organon. 

A diftributed term is marked by a horizontal line, 
with the letter S, P or M attached, to denote that it 
is the fubje£t, predicate or middle term of the fyl- 
logifm. 



An undiftributed term is marked, not by a definite 

line, but by a row of dots, to fhow its indefinitenefs, 

thus 

S... 

Thefe are the two forms of quantity in which fepa- 
rate conceptions may occur. But when two con- 
ceptions are joined in a judgment, another power as 
to quantity muft be reprefented alfo. Let the judg- 
ment be, " All plants are organized," and let the 
lower line reprefent the fubjeft and the upper the 
predicate ; will this reprefentation convey the whole 

truth ? 

P 

S 

In one point it is inadequate, that the term " orga- 
nized" is not wholly indefinite. We mean indeed 
by it, only fome organized things ; but then one part 
of it is made definite by affirming it of plants. We 



LAWS OF THOUGHT. 239 

do not know how many, or what, individuals, come 
into the conception "Some organized things" by 
itfelf y but when it occurs in this judgment, we are 
certain of fome individuals in it, viz. thofe which are 
" all plants." This we are able to exprefs by a line 
partly definite, partly undetermined, thus 

P ....... 

S . 

Every affirmative judgment may be reprefented by a 
line drawn under another, the lower being always the 
fubje£t. Negative judgments, which exprefs that 
one conception cannot be contained under another, 
are reprefented by two lines drawn apart from each 
other, the predicate being a little higher than the 
fubjedt, thus — 



But in a fyllogifm there are three terms, fo that we 
require three lines to reprefent their relations \ and 
the diagram thus drawn will fupply fome important 
illustrations of the nature of inference. Suppofe the 
premifles are " All matter undergoes change, and the 
diamond is a kind of matter," the relations of the 
three terms may be thus exhibited. 

P.., 

M 



240 OUTLINE OF THE 

From this notation, befides the two premiffes given, 
i. All M is P 

2. All S is M 

we may, by reading downwards, gather that 

3. Some P is M, and 

4. Some M is S 

which are in fa£t immediate inferences by conver- 
fion from each of the premiffes refpeftively. But 
further, from knowing that M ftands under P, and 
S under M, we have learnt that S ftands alfo under P, 
and this we may exprefs, leaving M altogether out 
of our ftatement, 

5. All S is P 

6. Some P is S, 

the former being the proper conclufion from our pre- 
miffes, and the latter the converfe of the conclufion. 
Where one premifs is negative, and by the canon 
of fyllogifm one only can be of that quality, the nota- 
tion will be 

P 

M... ... 

S 

which would be read thus, 

No M is P 
All S is M 
Therefore, No S is P. 



LAWS OF THOUGHT. 

Finally, every univerfal judgment of fubftitutic 
or U, may be exprefled by two equal lines 

p 

S 

But when fuch a judgment exprefles a logical divi- 
fion, as " Organized beings are either plants, brutes 
or men," the divided charafter of the predicate may 
be exprefled by breaking up the line which repre- 
fents it, thus 

P x — i y z 

S 

which would be read, " All S is either x y or z." 
The contrary procefs, of logical compofition, which 
is ufed to exprefs induction, as " Plants, brutes, and 
men are the only organized beings" would appear as 

P 

S x y z 



and be read "xyz make up the fum of P." — The 
reader will find great advantage in comprehending 
the rules of fyllogifm, from figuring the iyllogifms to 
which they happen to apply, according to thefe di- 
rections.* 



* This fcheme of notation has been improved by Sir William 
Hamilton, but the view in the text is quite fufficient for our pre- 
fent purpofe. 



242 OUTLINE OF THE 

§ 102. Equivalent Syllogifms. 

Though the Reduction of Syllogifms, from a fo- 
called imperfeCt, to the perfect, figure, is no longer 
requifite, now that the power of the diclum de omni 
et nulla is confined to the proper limits, the relations 
of three conceptions can be expreffed, commonly, in 
more than one fyllogifm of the fame figure, and al- 
ways in different figures. And the advantage of any 
adequate fyftem of notation is that it not only repre- 
fents to us the fyllogifm itfelf, which is one way of 
ftating the mutual bearing of three conceptions, but, 
in making that mutual bearing vifible, it furnifhes 
the means of ftating it in other fyllogifms. An ex- 
ample will illuftrate this. 

" No agent more effectually imitates the natural 
action of the nerves, in exciting the contraCtility of 
mufcles, than Electricity tranfmitted along their 
trunks, and it has been hence fuppofed, by fome phi- 
lofophers, that eleCtricity is the real agent by which 
the nerves aCt upon the mufcles. But there are 
many objections to fuch a view ; and this very im- 
portant one among the reft, — that electricity may be 
tranfmitted along a nervous trunk which has been 
comprejfed by a Jlring tied tightly round it, whiljl the 
paffage of ordinary nervous power is as completely 
checked by this procefs, as if the nerve had been di- 



LAWS OF THOUGHT. 243 

vided."* This argument may be thrown into the 
following fyllogifm, as the moft direct form of ftate- 
ment. 

Ele&ricity will travel along a tied nerve, 
The nervous fluid will not travel along a tied nerve j 
. * . The nervous fluid is not ele6hricity. 

This is a fyllogifm in the fecond figure, and of the 
mode A E E, which will be found in the Table in 
the preceding fection, and is therefore a valid mode. 
The middle term is the conception " able to travel 
along a tied nerve ;" and one of the other terms is 
under it, and the other not, fo that they cannot agree; 
and this mutual relation may be conceived by the 
following lines : — 

M 

p S 



The queftion now is — whether having obtained this 
relation, we cannot find other modes, befides A E E, 
Fig. ii. in which to exprefs it. 

As the phyfiologift is moft engaged with the parts 
and functions of the animal economy, to him " The 
nervous fluid" would be the moft prominent term, 
the fubjecT: of thought, and therefore would very 
properly be the fubjeft of the whole fyllogifm. But 
the fame three conceptions would be the grounds for 
arguing — 

* Carpenter. Animal Phyfiology, p. 437. 



244 OUTLINE OF THE 

The nervous fluid will not travel along a tied nerve, 
Electricity will travel along a tied nerve ; 
. \ Electricity is not the nervous fluid. 

This is E A E, Fig. ii. which is alfo a valid mode; 
and it would befl: fait one who was examining elec- 
tricity. It is the fame as the laft ftatement, except 
that the prefent is the converfe of the former con- 
clufion. Again, though fomewhat lefs naturally, we 
may ftate it, 

Nothing that travels along a tied nerve can be the nervous 

fluid, 
Electricity travels along a tied nerve $ 
. \ Electricity cannot be the nervous fluid. 

This is E A E, of the firft Figure. From what has 
been faid we fee that the relations between any three 
conceptions in our mind are permanent; that the 
expreffion of them is not permanent, but may now 
affume one mode of fyllogifm, now another; that 
the conditions which determine us to one form as 
more natural than another are, partly, the difference 
of extenfion in the conceptions, where it is afcertain- 
able, partly the greater prominence of one concep- 
tion in our thoughts at the time, which entitles it to 
be the fubjeft ; that any one of the fyllogifms founded 
on the conceptions is fufficient to afcertain their re- 
lations ; and that by a fcheme of notation we may 
reprefent, not merely one of the cognate fyllogifms, 



LAWS OF THOUGHT. 245 

but the ground of all of them, from which they can 
afterwards be drawn out feparately. 



§ 103. Sir William Hamilton's Scheme of Modes 
and Figures of Syllogifms. 

A mode of notation propofed by Sir William Ha- 
milton is, beyond doubt, one of the moft important 
contributions to pure Logic which has ever been 
made fince the fcience was put forth ; and I am for- 
tunate in being permitted to annex it. # Its excel- 
lencies are — that it is very fimple, that it fhows the 
equivalent fyllogifms in the different figures at a 
glance, that it fhows as readily the convertible fyllo- 
gifms in the fame figure, that it enables us to read 
each fyllogifm with equal facility according to exten- 
fion and intenfion, the logical and the metaphyfical 
whole. 

In this Table M denotes the middle term ; and 
C and T the two terms of the conclufion. A colon (:) 
annexed to a term denotes that it is diftributed, and 
a comma (,) that it is undiftributed. Where the 
middle term has a : on the right fide, and a , on the 
left, we understand that it is diftributed when it is 

* It is alfo to be found in Mr. T. Spencer Baynes* New 
Analytic. But the order of the Moods is different, and the 
prefent order is that finally fixed on by Sir W. H. 



246 OUTLINE OF THE 

coupled in a judgment with the term on the right, 
and undiftributed when coupled with the other. 

The fyllogifms actually reprefented are all affirma- 
tives, being twelve in each figure ; and the affirma- 
tive copula is the line — — , the thick end denoting 
the fubjecft, and the thin the predicate, of extenfion. 

Thus C : , M would fignify « All C is (feme) 

M." In reading off the intenfion, the thin end de- 
notes the fubjeft. 

But from each affirmative can be formed two ne- 
gative fyllogifms, by making each of the premifles 
negative in turn. The negation is exprefled by draw- 
ing a perpendicular ftroke through the affirmative 
copula; thus ■■ | . In the negative modes the dif- 
tribution of terms will remain exaftlv the fame as it 
was in the affirmatives from which they were re- 
fpe£tively formed. 

The line beneath the three terms is the copula of 
the conclufion ; and in the fecond and third figures, 
as there may be two conclufions indifferently, a line 
is alfo inferted above, to exprefs the fecond of them. 

The mark K — v — ' under a mode denotes that 
when the premifles are converted, the fyllogifm is 
ftill in the fame mode. 

But a ^^^ between two modes, fignifies 
that when the premifes of either are converted, the 
fyllogifm pafles into the other. 



LAWS OF THOUGHT. 247 

The middle is faid to be balanced when it is diftri- 
buted in both premifTes alike. The extremes, or 
terms of the conclufion are balanced, when both 
alike are diftributed ; unbalanced, when one is and 
the other is not. 

According to this fcheme there are 12 affirmative 
Moods in each Figure, and 24 negatives, or 36 alto- 
gether. All the pojjible moods of fyllogifm are here 
exhibited ; but the value of the inference in fome of 
them is fo fmall that they would never a£tually be 
employed. For example, by making negative the 
firft premifs of No. v. Fig. 11. we have fuch a fyllo- 
gifm as — 

Some ftones do not refift the action of acids, 
Some metals refift the action of acids 5 
.*. Some metals are not fome ftones, — ■ 

where there is undeniably an inference, but one 
which can fcarcely be faid to add to our knowledge 
of the fubjeft of it. To facilitate a comparifon of 
this Table with the former one (p. 236) its Moods 
are tranjlated into equivalent letters ; and an exami- 
nation will prove that every mood not containing the 
vowel y\ or a,* occurs in both tables, which after de- 



* The objections to the employment of the judgments de- 
noted by this will be found at p. 178, together with the grounds 
on which they have been defended. See Sir W. Hamilton's 



248 



OUTLINE OF THE 



Table of Modes. 





Fig. i. 


Fig 


. 11. 


Fie 


;. in. 


Aff. 


Neg. Aff. 


Neg. Aff. 


Neg. 


i 


uuu 


EU E 
UEE 


UUU 


E U E 
UEE 


UUU 


E UE 
UEE 


ii 


A YI 


n Y « 
A O a; 


YY I 


O Y ft? 
YO ft? 


AA I 


» A 00 

A » 00 


iii 


AAA 


n A n 

Ann 


YAA 


O A n 

Y n « 


AYA 


n Y n 

A O q 


iv 


YYY 


OYO 
YOO 


A YY 


* Y O 
AOO 


Y AY 


O AO 

Y n O 


V 


All 


n I 00 
A ft? a> 


Y I I 


O I ft? 
Y a? &? 


All 


u I 00 
A ft? a? 


vi 


I Y I 


a? Y 00 
I O « 


I Y I 


&? Y &? 
I O ft? 


I A I 


ft? A ft? 
I « a? 


vii 


UYY 


E YO 
U O O 


UYY 


E YO 
U OO 


U AY 


E A O 

U n O 


viii 


AUA 


« U n 
A E n 


YU A 


O U « 

YE n 


AUA 


n U n 
AE q 


ix 


UAA 


E A E 

U n n 


UAA 


E AE 

U n ti 


U YA 


EYE 
UO O 


X 


YU Y 


OUO 
YEE 


AUY 


n UO 
AEE 


YU Y 


OUO 
YEE 


xi 


U I I 


E I O 

U ^ a? 


U I I 


E I O 

U ft? ft? 


U I I 


E I O 
U a? O 


xii 


I U I 


a? E 00 
I U n 


I U I 


&? U a? 
I E n 


I U I 


a? U a? 
I E n 



Sum of all the valid Modes in each Figure. 



This Table. Former Table. 

1. 36 (— 12 aff. + 24 neg.) — 14 weak neg. zz 22 
ii. 36 (=z 12 aff. + 24 neg.) — 16 weak neg. n 20 
in. 36 (— 12 aff. + 24 neg.) — 15 weak neg. — 21 



LAWS OF THOUGHT. 249 

dueling the difputed moods fo marked, coincide in 
all refpe&s. 

§ 104. Euler' s Syjiem of Notation. 

Perhaps the moft celebrated plan of notation is 
that which Euler has defcribed in his Lettres a une 
princeffe d'Allemagne.* But, as it only reprefents 
the extenfion of the terms, and not the oppofite ca- 
pacity, of intenfion, it is inferior to that which has 
juft been defcribed. The fphere of a conception is 
reprefented by a circle ; an affirmative judgment by 
one circle wholly or partly contained in another ; 
and a negative by two feparate circles. The judg- 
ment that " All men are mortal" has the effect of 
including men in the clafs of mortal beings, which 
would be reprefented by a fmall circle for " men," in 
a large one for " mortal." The annexed diagram ex- 
hibits (1) the Mood AAA, (11) E A E, (111) A 1 1, 
and (iv) E I O, all of the firft Figure. 

§ 105. Inference in Intenfion and Extenfion. 
That a judgment may be interpreted either in its 



Note in Mr. Bay ties' 1 New Analytic, p. 153, and Difcuffions in 
Philofophy, p. 614, by the fame author, for further elucida- 
tions of this fyftem. 

* Made known before Euler by Lange in his Nucleus Lo- 



250 



OUTLINE OF THE 







LAWS OF THOUGHT. 251 

extenfion or intenfion has been already fhown (§ 80). 
Every fyllogifm has the fame property. Thus, 

All metals are luftrous, 
Iridium is a metal ; 
/. It is luftrous — 

may either be read in extenfion 

The clafs of metals are fome luftrous things, 
Iridium is in the clafs of metals $ 
.'. Iridium is among luftrous things — 

or in intenfion 

The notion of fome luftrous things attaches to the notion of 
all metals, 

The notion of fome metal is implied in Iridium ; 
.•. The notion of fome luftrous thing attaches to that of Iri- 
dium — 

or in lefs uncouth, but at the fame time, lefs accu- 
rate form — 

Luftroufnefs belongs to our notion of metals, 
Being a metal is part of the notion of Iridium 5 
.*. Luftroufnefs belongs to our notion of Iridium. 

Although any argument may be fo exprelTed as to 
give the one or the other capacity greater prominence, 
it is at all times poffible to read an argument in both 



gica We'ifiana, 17 12, and apparently firft employed by Chrift. 
Weife, who died in 1708. Ploucquet employed the fquare, and 
Maafs the triangle inftead of the circle. Drobifch Logik. § 84.. 



252 OUTLINE OF THE 

its powers, preferving of courfe the diftribution of 
terms unchanged. The moft important term in the 
extenfive point of view is the leaft in the intenfive, 
becaufe it embraces moft obje£ts, but we know leaft 
of its nature ; in the example, "luftrous" contains the 
other terms under it, and more, but " iridium" im- 
plies in it the notion of luftrous and much more ; 
" luftrous " therefore has the greateft extenfion, 
" iridium" the greateft intenfion. Where the terms 
are equal, as in U U U of all Figures, extenfion and 
intenfion are in aquilibrio. 

§ 1 06. Conditional Syllogifms. 

A fyllogifm in which there is one pure conditional 
judgment or more (fee p. 160,) is called a Conditional 
Syllogifm. All arguments of this clafs come into the 
fcheme of fyllogifms already given, when they are 
properly exhibited. The principal forms are here 
annexed. 

1. In cafes where M is N, C is D, 

In cafes where A is B, M is N ; 

. • . In cafes where A is B, C is D. 

11. In cafes where C is D, M is N, 

In cafes where A is B, M is N 5 

. • . In cafes where A is B, C is D. 

in. In cafes where M is N, C is D, 
In cafes where M is N, A is B ; 
. • . In cafes where A is B, C is D. 



LAWS OF THOUGHT. 253 

Thefe three forms are compofed entirely of con- 
ditional propofitions. They are in the three different 
figures ; and examples of them will be corredt or in- 
correct according as they do or do not conform to 
the principles of the fyllogifm already laid down, as 
to affirmation and negation, diftribution of terms, &c. 

iv. In cafes where M is N, C is D, 
But in the given cafes M is N $ 
Therefore in thefe cafes C is D. 

v. In cafes where M is N, C is not D, 
But in the given cafes M is N$ 
Therefore in the given cafes C is not D. 

vi. In all cafes where M is N, and in no others, C is D, 
In the given cafes, M is not N ; 
Therefore in the given cafes C is not D. 

VII. In all cafes where M is N, and in no others, C is D, 
In the given cafe C is D $ 

Therefore M is N. 

viii. In all cafes where A is B, M is N, 
In the given cafes M is not N j 
Therefore in the given cafes A is not B. 

ix. In all the cafes where A is B, M is not N, 
In the given cafes M/;N; 
Therefore in the given cafes A is not B. 

It may facilitate the ufe of thefe formulae if con- 
crete examples of them are added, exprefled in the 
form of ordinary categorical fyllogifms. 



254 OUTLINE OF THE 

i. (A A A. Fig. i.) 

All cafes where law prevails, are cafes where the rights of the 

weaker are fecured, 
All well-ordered ftates exhibit fuch cafes •> 
Therefore in all well-ordered ftates, the rights of the weaker 

are fecured. 

ii. (A E E. Fig. ii.) 

All cafes where rain falls are cafes where clouds obfcure 

the fky, 
All cafes of heavy dew are cafes where there are no clouds 5 
Therefore cafes of heavy dew are not cafes of rain. 

in. (A AI. Fig. hi.) 

All cafes of ignorance are cafes in which a crime is excufed, 
Such cafes are inftances of an abfence of will or intent 5 
Therefore fome cafes of abfence of will are cafes in which 
crimes are excufed. 

iv. (A A A. Fig. i.) 

The fuppofition that matter cannot move of itfelf implies the 

exiftence of a higher moving power, 
What we adopt is the fuppofition, &c. 5 
Therefore we adopt the view that a higher moving power 

exifts. 

v. (E A E. Fig. i.) 

The fk£k that the moon prefents always the fame face to the 
earth implies that fhe has no diurnal revolution on her 
axis, 
But fhe does prefent the fame face to the earth 5 
Therefore Hie cannot go through the diurnal revolution. 



LAWS OF THOUGHT. 255 

vi. (U E E. Fig. i.) 

All the times when the moon comes between the earth and the 

fun, are the fole cafes of a folar eclipfe, 
The nth of February is not fuch a time ; 
Therefore the 1 1 th of February will exhibit no eclipfe of the 

fun. 

vii. (U A A. Fig. i.) 

All the times when the earth's fhadow falls on the moon, are 

the fole cafes of lunar eclipfe, 
The 7th of July is fiich a time ; 
Therefore the 7th of July will be the occafion of an eclipfe. 

viii. (A E E. Fig. ii.) 

The cafe of the earth being of equal denfity throughout would 

imply its being i\ times as denfe as water, 
But in fa£l it is not 2 J times as denfe as water, but 5f times 5 
Therefore it is not of equal denfity. 

ix. (E A E. Fig. ii.) 

No cafes of excemVe dew are cafes of cloudy night, 

But this night is cloudy 5 

Therefore the dew will not be exceflive. 

Other modes might be added, but thefe may fufKce 
to exhibit the nature of the conditional fyllogifm, 
together with its affinity to the regular forms. That 
peculiar connexion between two fa£ts which confti- 
tutes the one caufe and the other effect, offers a 
problem worthy of the ftudy of the metaphyfician.* 

* The principal opinions upon the fource of our idea of 
caufe and effect may be thus Sketched : 

i. Locke refers this idea to fenfation. We fee that one thing 



256 OUTLINE OF THE 

But that the two are connected, and that their re- 
lation refembles in many particulars that offubje£t 
and predicate in an ordinary propofition, is all that a 
logician need afcertain. An ordinary proposition af- 
ferts that the thought of one thing or attribute draws 
with it, or implies, the thought of another thing or 



has the power to create, or generate, or make, or alter another 
thing, and fuch powers we call caufing, and the things that 
have them are caufes. Hum, Und. ii. 26. §2. 

ii. Hume rejects the notion that the fact which we call a 
caufe exercifes any power whatever over the effect. But from 
conftantly obferving the affociation or fequence of two facts, 
we begin to fee their invariable connexion, and to reprefent 
one as the caufe of the other. (Effays, vol. ii. p. 86.) A num- 
ber of obfervations is thus a neceffary condition of our forming 
this idea. But why do we give it a name that diftinguifhes 
it from fequence, if it is mere fequence ? The funfet always 
follows a flood tide, at a greater or lefs interval 5 but no one 
affociates them under the idea of caufation. 

iii. Leibniz afligns to' everything that exifts a certain force 
or power, and thus conftitutes it a caufe. Exiftence, indeed, is 
meafured by power. Whilft Locke, as Hume remarks, infers 
caufation from the fact that things come into being and are 
changed, Leibniz regards power and caufation as primary 
attributes of all being, not inferred from but implied by it. 
Nowveaux Eflhis, B. 11. 

iv. Kant confidered the notion of caufe and effect as one of 
the forms of the underftanding, one of the conditions under 
which we rauft think. We are compelled by a law of our 
mind to arrange the impreflions of our experience according to 
this form, making one thing a caufe and another an effect 5 



LAWS OF THOUGHT. 257 

attribute ; the conditional judgment declares that the 
thought of one fa£t brings with it the thought of 
another fa£t; but whether the connection of the 
fa&s is fuch as to invert them with a particular pro- 
perty, or arifes only in the mind, and is one of the 
forms of thought under which the mind views ex- 



but whether there exifts in the objects themfelves that which 
we mean by a caufe and an effect, we cannot determine. {Cri- 
tique, Tranfcendental Analytic.) 

v. The view of Maine de Biran is chiefly known through 
the writings of ViBor Coujin and others. According to him 
(and I quote through his critics only) the notion of caufe 
originates with our confcioufnefs of the power of will, which 
recognizes the will as the caufe of our actions j and we transfer 
this perfonal power by a kind of analogy to all the operations 
of nature. 

vi. Sir William Hamilton traces the idea of caufality to that 
limitation of our faculties which prevents us from realizing an 
abfolute commencement or an abfolute termination of being. 
When we think of a thing, we know that it has come into 
being as a phenomenon, but we are forced to believe that the 
elements and facts that produced the phenomenon exifted already 
in another form. In the world to which our obfervations are 
confined, being does not begin j it only changes its manifesta- 
tions; the flock of forces (fo to fpeak) is not augmented, 
though their direction and operations alter. By our idea 
of caufation we exprefs this belief 5 the caufes of anything 
are the forces and elements of it, before they took fhape in it. 
But fee an admirable Confpectus of the theories of Caufality 
with a much fuller account of his own view in Sir W. Ws 
Difcuflions, &c. p. 58 5, fol. 

S 



258 OUTLINE OF THE 

ternal impreffions, we fhall not enquire. If the in- 
ferences in the categorical fyllogifm might be defcribed 
by the principle Not a noted eft nota rei ipfius (fee 
p. 226), the correfponding form of conditional fyllo- 
gifm would be explained by Effettus effettus eft ef- 
feSfus caufa. And fo throughout might the parallel 
be traced between every categorical mode and a 
parallel hypothetical. 

One diftin&ion of caufes muft not be forgotten, 
that which is between the caufe of our knowing a 
faft [caufa cognofcendi)^ and the caufe of the faft's ex- 
iftence (caufa ejfendi). When we fay "the ground 
is wet, becaufe it has rained," we affign to the rain 
the latter character ; it is the caufe of the ground ac- 
tually being in this ftate. But the caufe may change 
places with the effe£t ; " it has rained becaufe the 
ground is wet"— -where the wetnefs of the ground is 
the caufe of our being Jure there has been rain, and 
this is all that we mean to aflert, and not the abfurd 
propofition that the wetnefs, which followed, could 
bring about the rain which preceded. The enquiry 
into caufes which occupies the induilive philofopher 
applies to caufes of things being, and not properly to 
caufes of our knowing things. 



LAWS OF THOUGHT. 259 

§ 107. DisjunSfive Syllogifms. 

An argument in which there is a disjunctive judg- 
ment (p. 159) is called a disjun&ive fyllogifm. A 
pure disjunctive argument (i. e. one in which no im- 
mediate inference has to be fupplied) may be at once 
referred to its proper mode, by afcertaining the quan- 
tity and quality of the disjunctive judgment in it. 
The principal forms of fuch fyllogifms are annexed. 

1. (In A U A. Fig. 1.) 

C D and E are P, 
All Sis either CD or E; 
.-. All S is P. 

2. (In E U E. Fig. 1.) 

Neither C nor D nor E is P, 
All S is either C or D or E ; 
.\ S is not P* 

3. (In U E E. Fig. 11.) 

All P is either C or D or E, 
S is neither C nor D nor E ; 
.*. S is not P. 

4. (In E U E. Fig. 11.) 

P is neither C nor D nor E, 
S is either C or D or E ; 
.-. S is not P. 



260 OUTLINE OF THE 

5. (In I A I. Fig. in.) 
Either A B or C is P>* 
A B and C are S ; 

.\ Some S is P. 

6. (In A U A. Fig. 111.) 
C D and E are B > 

C D and E = A 
.\ A is B. 

Concrete examples of thefe forms are — 

1 . Solid fluid and aeriform bodies are elaftic, 
Every body is folid, fluid or aeriform 5 
Therefore every body is elaftic. 

2. Neither England, Ireland, Scotland nor Wales is un- 

healthy, 
All Great Britain is either England, Ireland, Scotland 

or Wales 5 
Therefore Great Britain is not unhealthy. 

3. A fcience is either a pure, induclive or mixed fcience, 
Aftrology is none of thefe 5 

Therefore Aftrology is not a fcience. 

* This is really a particular affirmative judgment (I) 5 for it 
means that "Some of A B C are P." It muft not be con- 
founded with its apparent converfe. " P is either A B or C" 
which is a univerfal fubftitutive judgment (U) and means that 
P is divifible into A B and C. Thus " a primitive colour 
muft be blue, red or yellow'' is converted into " blue, red and 
yellow are the primitive colours," and not into " either blue 
red or yellow is a primitive colour." 



LAWS OF THOUGHT. 261 

4. A queftion neither affirms nor denies, 
A judgment muft affirm or deny $ 
Therefore a judgment cannot be a queftion. 

5. Either Chriftianity or Judaifm or Mohammedanifm is the 

true religion, 
Chriftianity, Judaifm and Mohammedanifm are alike rao- 

notheiftic j 
Therefore a monotheiftic religion is the true one. 

6. Oxygen, hydrogen, chlorine, Sec. are lighter than water, 
Oxygen, hydrogen, chlorine, &c. are the whole of the 

gafes j 
Therefore all the gafes are lighter than water.* 

The complex disjunctives are founded upon the 
law of diftinft divifion already ftated (p. 109). If 
a genus is divided into fo many fpecies, what is in 
one of the fpecies cannot be in another. In bring- 
ing them into the form of common fyllogifms, we 
need only employ a new premifs, gained by an im- 
mediate inference under this very principle (p. 212). 
Thus — 

All A is B or C, 

This A is not B ; 
.*. This A is C — 
would become 



* This is the formula for the Induction by fimple Enume- 
ration, where on finding a property to belong to every mem- 
ber of a clafs fingly, we infer that it belongs to the whole 
clafs. The worth of fuch an argument is confidered below. 



262 OUTLINE OF THE 

[All A is B or C, therefore] 
All (A that is not B) is C, 
This is an (A that is not B ; 
.\ This is C. 

All fciences are either pure, inductive or mixed fciences, 
Aftronomy is not a pure or inductive fcience 5 
.*. It is a mixed fcience — 

would ftand as a fyllogifm in A A A. Fig. 1. 

Sciences that are not pure nor inductive are mixed, 
Aftronomy is a fcience not pure nor inductive ; 
Therefore it is a mixed fcience. 



§ 108. Complex Syllogifm. Sorites. 

The fimple fyllogifm is the type of all reafoning, 
and the teft to which all reafoning may be brought* 
But there are more complex forms of argument, not 
lefs natural than the fyllogifm itfelf, which do not re- 
quire to be reduced to fyllogifms to fhow their cor- 
re&nefs, jufl: as we know ice to be ice without re- 
ducing it to the needle-fhaped cryftals with which 
freezing commences. Of this kind is the Sorites. 

Three or more premifles in which the predicate of 
each is the fubjeft of the next, with a conclufion 
formed from the firft fubjeft and laft predicate of 
the premifles, have been called a Sorites, or accumu- 
lating argument, from the Greek word crag c£, a heap, 



LAWS OF THOUGHT. 263 

The name is not very appropriate \ the German title 
of chain-argument (kettenfchlufs) exprefles better the 
nature of a procefs in which the mind goes on from 
link to link in its reafoning, without thinking it ne- 
ceflary to draw out the conclufions as it paries. 
Where the premifTes are all univerfal affirmative at- 
tributive judgments, not the leaft confufion can arife 
from thus poftponing till the end the realization of 
the refults. But where the premifTes are judgments 
of different kinds, the reafoning is more difficult to 
follow, and it may be neceflary to draw out each fyl- 
logifm feparately, in order to fee whether it is in a 
valid mood, and, if otherwife, what is the fault in it. 
This is done as follows. 

All the premifTes but the firfl are leading premifTes 
of fo many diftinct fyllogifms -, therefore there are 
as many fyllogifms, minus one, as the Sorites has pre- 
mifTes. For the fecond premifs of the firft fyllogifm 
the firft judgment of the Sorites muft be taken ; 
whilft to each fucceeding one the conclufion of its 
predeceflbr muft be the fecond premifs. A diagram 
will make this much clearer. 

1. A is B, 

2. B is C, 

3. C is D, 

4. D is E, 
Therefore A is E. 



264 OUTLINE OF THE 

Reduced to 

i. ii. ii. 

2. B is C, 3. C is D, 4. D is E, 

1. A is B, [A is C], [A is D], 

[,\ A is C.] ? [.-. A is D], [.\ A is E.] 

Thefe fyllogifms are all in A A A. Fig 1. a valid 
mode. An invalid mode occurring before the laft 
fyllogifm would not only be wrong itfelf, but, as fur- 
nifhing a premifs to its fucceflbrs, would vitiate every 
fyllogifm that follows. 

The number of conclufions which thefe premifles 
admit of, is greater than a&ually appears. We may 
conclude A C, A D, A E (which appear;) and B D 
B E, C E. Five premifles inftead of four would in- 
creafe the number of conclufions to ten.* There is a 
form of the Sorites to which the name of Goclenius 
its inventor has been attached, which is the fame as the 
common form, except that the premifles are reverfed, 
It would run 

DisE, 

CisD, 

BisC, 

A is B, 
.\ A is E. 

* Com. Arift. Pri. An. 1. 25. The formula for afcertain- 
ing the number of conclufions is this. 

Let the number of premifles z~ n, the number of terms 
zz n -}- 1 ; then the number of conclufions zn (n — 1 ) 

1.2 



LAWS OF THOUGHT. 



265 



In the Goclenian Sorites extension is made more pro- 
minent, by ftarting with the premifs which has the 
two wideft terms ; in the common form intenfion 
predominates, as the narrower terms precede. The 
former defcends in extenfion from the predicate of 
the conclufion ; the latter afcends in intenfion, from 
the fubjeft. The Goclenian form fuits deduftion 
beft ; the common or Ariftotelian form, induftion. 
The Goclenian defcends from law to fa£t ; the com- 
mon afcends from fa& to law.* 

This will be clearer from a pair of examples. 



GOCLENIAN OR DESCENDING 
SORITES. 

Sentient beings feek happi- 

nefs, 
All finite beings are fentient, 
All men are finite beings, 
Caius is a man ; 
Therefore he feeks happinefs. 



ARISTOTELIAN OR ASCEND- 
ING SORITES. 

Caius is a man, 
All men are finite beings, 
All finite beings are fentient, 
All fentient beings feek hap- 
pinefs 5 
Therefore Caius feeks happi- 
nefs. 



* A " pretty quarrel" long exifted amongft logicians, which 
of the two was to be called progrejfive and which regrejfi<ve> 
Till Kanfs time, the Goclenian was called progreflive, the com- 
mon regreffive. Kant reverfed it, followed by Kief enfetter and 
others. Jacob reverfed it again, followed by Krug and others, 
Troxler ii. 100. A mere ftrife about words. If we are dis- 
covering truth by the inductive method, the Ariftotelian form is 
progreflive 5 if we are teaching truth, or trying our laws upon 
new facts, we ufe deduction, and the Goclenian form is pro- 
greflive. In an apt but familiar figure — if I am on the ground 



266 OUTLINE OF THE 

In the following example a mixed order prevails : 

That which thinks is active, 
That which is a<5Kve has ftrength, 
That which has ftrength is fubftance, 
The foul thinks 5 
Therefore it is fubftance. 

The premifles of the Sorites may be, all or fome 
of them, hypothetical ; indeed as this argument is but 
an aggregation of fimple fyllogifms, the rules for the 
conftru&ion of fimple fyllogifms apply to its feveral 
parts ; with this one caution, that in the Sorites each 
foregoing fyllogifm furnifhes a premifs, not exprefTed, 
to the next fucceeding one, and therefore we muft 
fee not only that each is good in itfelf, but that it will 
furnifli an available premifs to its fucceffor. This 
may be tried by altering one of the higher premiffes 
in any of the examples into a negative ; at the next 
ftep, an error will be apparent. 

§ 109. The Dilemma. 

The Dilemma is a complex argument, partaking 
both of the conditional and disjunctive. It is a fyllo- 

floor, and wifh to fetch fomething that is above, my going up- 
ftairs is my progrefs towards my obje£t, and my coming down 
is a regrefHon $ if the pofitions of myfelf and the thing are re- 
verfed, going down would be progrefs, and returning up, 
regrefs. The indu6live truth-feeker is on the ground-floor of 



LAWS OF THOUGHT. 267 

gifm with a conditional premifs^ in which either the 
antecedent or confequent is disjunctive. It may prove 
a negative or an affirmative conclufion ; in the for- 
mer cafe it is faid to be in the mode of removal 
[modus tollens) becaufe it removes or refutes fome 
conclufion that has been propofed for proof: in the 
latter it is in the mode of pofition [modus ponens) 
becaufe the propofed queftion is laid down^ as proved. 
The following forms of it, with the manner in which 
they are prefented as fyllogifms, may be fufficient. 

1. 

If A is B or E is F, then C is D, 
But either A is B or E is F 5 
,\ C is D. 

11. 
If A is B, then C is D or E is F, 
But neither C is D nor E is F 5 
.-. A is not B. 

in. 

If fome A is B, either the m that are A or the n that are B, 
But neither the m that are A nor the n that are A are B 3 
.-. A is not B. 

The fame regarded as fimple fyllogifms. 

1. 
[The cafes of A being B and E being F] are [cafes of C 
being D], 

fa6ls, and goes up to feek a law 5 the deductive teacher is on a 
higher ftory, and carries his law down with him to the fa<5ls. 



268 OUTLINE OF THE 

This is [a cafe of A being B or E being F] 5 
.*. This is [a cafe of C being D]. 

11. 
[The cafe of A being B] is [a cafe of C being D or E 

being F]. 
This is not [a cafe of C being D or E being F] ; 
.'. This is not [a cafe of A being B]. 

in. 
Neither m of A nor n of A are B, 
All A is either m or n 5 
.-. No A is B. 

The word Dilemma means " double propofition," 
fo that the whole argument takes its name from the 
one mixed judgment in it. When this is more than 
double, as in " If a prifoner is legally difcharged, 
either the magiftrate muft refufe to commit, or the 
grand jury ignore the bill, or the common jury acquit, 
or the crown exercife the prerogative of pardon," 
the argument has been called a Trilemma, Tetra- 
lemma, or Poly lemma, according to the number of 
members the judgment may have. 

The following are concrete examples of the for- 
mulae. 

I. If the king is moved or if he is covered, I am check- 
mated the next move. One or the other muft be. Therefore 
I (hall be checkmated. 

II. If a man cannot make progrefs towards perfection, he 
muft either be a brute or a divinity 5 But no man is either, 
Therefore every man is capable of fuch progrefs. 

in. If fome fcience can furnifh a criterion of truth, either a 



LAWS OF THOUGHT. 269 

formal or a real fcience muft do fo. But (for different reafons) 
neither the formal fciences nor the real do fo $ Therefore, fci- 
ence affords no criterion of truth. 

Trilemma. If the fyftem of the univerfe is not the beft 
poflible, we muft fuppofe either that the Creator willed not a 
better one, or that he knew no better one, or that he could not 
create a better. The firft cannot be true (it is againft His good- 
nefs). The fecond cannot be true (it affails His wifdom). 
The third cannot be true (it limits His power). Therefore 
the fyftem of the univerfe is the beft. 

The popular notion of a Dilemma, that it is a 
choice of alternatives, each of them fatal to the caufe 
or the chara£ter of an adverfary, is countenanced by- 
many logicians, but can have no place in pure Logic, 
into which the obje£t to be gained by arguments, or 
the perfonal confequences which follow from admit- 
ting them, ought not to enter, and the properties of 
the arguments themfelves are the fole objedt of con- 
lideration. 

If the criminal knew the confequences of his acl, he was 
wicked 5 if he did not know the confequences, he was 
infane. 

This is really two diftin£t hypothetical judgments, 
aflbciated becaufe they happen to have a common 
term — " the criminal ;" and becaufe one or other 
of them muft be true ; and two diftincS: fyllogifms 
would be founded upon them, as the counfel for the 
defence would probably take for his fecond premifs — 
" He did not know the confequences of his aft, 



270 OUTLINE OF THE 

therefore he is infane," while the counfel for the pro- 
fecution would maintain that " He did know the 
confequences, and therefore was guilty." No doubt 
it is a great detriment to a prifoner to be found either 
guilty or infane, but this does not appear upon the 
face of the argument, and therefore pure Logic does 
not take it into account. A new judgment would be 
required to fhow the connexion of the two notions ; 
fo that befides the two conditional fyllogifms, con- 
tained in the argument itfelf, a third is tacitly ad- 
mitted, that fhows the connexion of the other two. 
This fort of argument, a great favourite with the So- 
phifts and old logicians, is called alfo Syllogifmus Cro- 
codilinus, and Syllogifmus Cornutus ; and " the boms of 
a dilemma" are known even to common language. 

§ HO. Incomplete Syllogifms, 

The arguments ufed in thinking, fpeaking or writ- 
ing, are never drawn out in ftri£t technical form, 
except by praftifed logicians, defirous of exhibiting 
their art to thofe who, like themfelves, are conver- 
fant with it. A fentence which contains the mate- 
rials of a fyllogifm, not technically exprefled, has 
been called an enthymeme, or an enthymematic fen- 
tence. Ariftotle underftands by enthymeme a fyllo- 
gifm fuch as would be ufed in rhetoric, where the 
full and orderly expreflion of premifles and conclu- 



LAWS OF THOUGHT. 271 

fion would feem laboured and artificial. And as 
the omiffion of one of the premifles is a common, 
perhaps the commoneft, feature of enthymemes, lo- 
gicians have defined them as fyllogifms with one 
premifs fuppreft. But we may alfo omit the con- 
clufion, or invert the order of premifles and conclu- 
fion ; and unlefs we extend the name enthymeme to 
thefe cafes we put a confiderable reftriction upon its 
original meaning. Let the enthymeme then be de- 
fined — an argument in the form in which it would 
naturally occur in thought or fpeech. 

§ ill. Profyllogifm and Epifyllogifm. 

In a chain of reafoning, one of the premifles of 
the main argument may be the conclusion of another 
argument, in that cafe called a profyllogifm : or the 
conclufion of the main argument may be a premifs 
to a fupplementary one, which is called an epifyllo- 
gifm. Let us take the fyllogifm which a coroner's 
jury might have to go through. The quejiion is 
"Has A. B. been poifoned?" and the fyllogifm is 
" A man who has taken a large quantity of arfenic 
has been poifoned, and A. B. is found to have done 
fo, therefore he has been poifoned ; " with the addi- 
tion of a profyllogifm and epifyllogifm the reafoning 
would run — " A man who has taken arfenic has 
been poifoned ; and A. B. has taken arfenic, for the 



272 LAWS OF THOUGHT. 

application of Marfh's and Reinfch's tefts difcover it 
(Profyl.); therefore A. B. has been poifoned, and 
therefore we cannot return a verdift of death from 
natural caufes. (Epifyl.) A profyllogifm then is a 
fyllogifm whofe conclufion is a premifs in a given fyllo- 
gifm ; an Epifyllogifm is one^ whofe premifs is a con- 
clufion in a given fyllogifm. The Sorites, Profyllogifm 
and Epifyllogifm, deferve our attention as the joints 
of thinking, by which the various members, the a£ts 
of immediate and mediate inference, are knit toge- 
ther in an organic connexion. Of them, however, 
the firft can rarely be employed ; the two laft meet 
us continually. 



OUTLINE OF THE LAWS 
OF THOUGHT. 

PART IV. 
APPLIED LOGIC. 

" Mais, parce que l'efprit fe lahTe quelquefois abufer par de 
fauflfes lueurs, lorfqu'il n'y apporte pas F attention neceffaire, 
et qu'il y a bien des chofes que Ton ne connait que par un 
long et difficile examen, il eft certain qu'il ferait utile d'avoir 
des regies pour Py conduire de telle forte, que la recherche de 
la verite en fut et plus facile et plus fure 5 et ces regies, fans 
doute, ne font pas impoflibles." 

Arnauld. 





APPLIED LOGIC. 

§ 112. Province of Applied Logic, 

N the foregoing pages the Laws of 
Thought have been confidered folely in 
themfelves ; and their connexion with 
the objects they belong to has been 
ftudioufly kept out of view. It has been fhown that 
every conception confifts of marks, without any at- 
tempt to explain how the marks are to be obtained ; 
that a judgment of a given quantity, quality and re- 
lation, can be converted or oppofed, no matter whe- 
ther it is a true judgment with reference to the 
matter it fets forth ; that a given form of fyllogifm 
is correct and its proof cogent, whether or no the 
premifTes it draws from are frivolous, or even incor- 
rect. In order to underftand aright the laws of 
thinking in themfelves, this procedure was neceflary ; 
for we muft diftinguifli between faults in the forms 
themfelves, which we have the means of correcting 
without travelling beyond them, and faults in the 



276 OUTLINE OF THE 

materials of thinking, that cannot be corrected with- 
out a reference to the objects that fupplied them. 
For example, u fome men are infallible," is a judg- 
ment correct in form, but falfe in matter, as our 
knowledge of humanity teaches us ; again to convert 
" fome men are philofophers," into " all philofophers 
are men," is wrong in form, although it happens that 
the latter judgment, erroneoufly produced, is mate- 
rially correct. 

Applied Logic (p. 7) teaches the application of the 
forms of thinking to thofe objects about which men 
do think. Thefe objects arrange themfelves under 
three great divifions, Man, the Univerfe, and Abfo- 
lute Being. When the views we take of objects are 
fubftantially correct, when our thoughts correfpond 
with facts, we are faid to be in poffeffion of the 
truth ; and thus we return to a definition of Applied 
Logic already propofed. It is the fcience of the 
neceflary laws of thought as employed in attaining 
truth. 

§ 113. Science. 

Thefe laws may be applied to the fragmentary 
knowledge and fcattered information gathered by 
every one in his paffage through the world ; they are 
unconfcioufly applied in this way every inftant. But 
it would be a higher application of them to erect by 
their means a complete ftructure of the truth that 



LAWS OF THOUGHT. 277 

related to one object or fet of objects, as Zoology 
contains all that relates to animals, Geology all we 
know of the earth's ftructure, and Pfychology all that 
pertains to the human mind and foul. Such a fyf- 
tem of the truths that relate to one fet of objects is 
called a fcience, which has been defined (p. 13), a 
fyftem of principles and deductions, to explain fome 
object matter. To fulfil its intention every fcience 
muft have attained to true ftatements concerning its 
object-matter, fo far as the nature of the cafe and 
the prefent means of examination allow ; it muft be 
able to define the object-matter, and its feveral fub- 
ordinate parts, with clearnefs and precifion ; and it 
muft be able to indicate the extent of the domain 
the object-matter covers ; and laftly it muft exhibit 
thefe refults in a fyftematic and harmonious fliape. 
For the firft it muft employ Induction and Deduc- 
tion ; the fecond is the province of Definition ; the 
third is provided for by Divifion ; and the fourth may 
be referred to Method. 

§ 114. Is a Philofophic Criterion of Truth pojfible. 

The fearch after truth cannot long difpenfe with 
any one of thefe inftrumentSj and even with the 
free ufe of them, the hiftory of fcience fhows how 
flow has been the advance, how largely (to ufe Leib- 
niz's image) the fand and mud of error have been 
mixed with the gold grains of truth. All of them 



278 OUTLINE OF THE 

in their degree have to do with evidence, with the 
proof of propofitions ; Indu&ion and Deduction 
chiefly with the difcovery and appreciation of evi- 
dence, and Definition and Divifion chiefly with the 
ftatement and arrangement of its refults. Hence, if 
we have to anfwer the queftion whether a Criterion 
of Truth, i. e. a ftandard for judging of the truth of 
propofitions, is poffible, # the anfwer that evidence 
is the fole means of eftablifhing, and therefore the 
fole ftandard for tefting, the truth of any propo- 
fition, and that all the operations connected with evi- 
dence contribute their fhare to the criterion. But 
fuch a maxim as that " a judgment muft reft 
upon fufficient evidence" is too abftraft to be of ufe 
by itfelf as a teft of truth. In fa£t no fhorter rule, 
no more portable touchftone can be indicated, for 
the examination of objective truth, than the whole 



* Plato fpeaks of " Experience, prudence and reafon," as 
affording conjointly a n^rh^ov of truth (Pol. 582. A). This for 
the fenfe of the word. For other propofed criteria, not men- 
tioned in the text, we have that of Wolff \ deter minabilit as prae- 
dicati per notionem fubjecli (but it applies only to explicative 
judgments — fee p. 185); that of Defcartes, "that is true, 
which is clearly known and perceived, " but he admits that the 
teft is fomewhat vague ; and laftly that of Plato, " truth is 
conformity with the ideas." Evidence is ufed by the Carte- 
fians fometimes in the fenfe of evidentnefs ; but we employ it 
to mean " the grounds which make evident." 



LAWS OF THOUGHT. 279 

fcience and rules of evidence. And in the fpecial 
cafes where other criteria appear to be applied, as in 
the difcuffion whether religious truth is to be tried by 
external teftimony or internal convi&ion, whether 
hiftorical evidence or the religious fentiment is the 
beft criterion, the difpute is only as to the kind of 
evidence that fhall take precedence. 

Four principal criteria of truth have been in dif- 
ferent forms advocated by logicians ; the reader is 
now in a pofition to eftimate their value. 

1 ft Criterion. The principle of Contradiclion. 
" The fame attribute cannot be at the fame time 
affirmed and denied of the fame fubje£t." Or "the 
fame fubje£t cannot have two contradictory attri- 
butes." Or " the attribute cannot be contradi£torv 

j 

of the fubje£t."* To illuftrate this — at a particular 
time fafts were obferved as to the motions of the 
planets, which were inconfiftent with the received 
theory, that thefe motions were circular. The the- 
ory was confequently modified, firft by the introduc- 
tion of epicycles, and finally by the fubftitution of the 
theory of elliptic revolution ; becaufe otherwife the 
aftronomer muft have affirmed of the planets a cir- 

* The firft mode of ftatement is Ariftotle 'j , to yap avro apa 

vir&pxeiv rs teal fxh vwapxeiv abvvarov r& avrZ xal Kara to avro. Me- 

taph. IV. (r.) lii. The fecond is Ariftotelian ; the third is 
Kanfs. 



28o OUTLINE OF THE 

cular and a non-circular motion, or in other words 
muft have affigned to a fubje£t, to which he had 
already given " circular motion," a predicate contra- 
dictory of this. 

2nd Criterion. The principle of Identity. 
" Conceptions which agree can be united in thought, 
or affirmed of the fame fubjeft at the fame time." 
This principle is the complement of the former. 

3rd Criterion. The principle of the Middle 
being excluded (lex exclufi medii). " Either a given 
judgment muft be true, or its contradictory ; there is 
no middle courfe." # So that the proof of a judgment 
forces us to abandon its contradictory entirely, as 
would the difproof of it force us upon a full accep- 
tance of the contradictory. This law, among other 
ufes, applies to the dialectical contrivance known to 
logicians as reduclio per impojjibile. 

4th Criterion. The principle of fufficient (or 
determinant +) reafon. u Whatever exifts, or is true, 

* This is the avriBscr^ %$ ova 'itrn (XBra^v HaB'civTWy of Ariftotle* 
(An. Poft, I. i. icaQ'avrriv " as appears per fe from the nature 
of the afTeriion." Trend.) Compare Metaph. IV. (r) 7, and 
Alexanders comment. 

f C. A, Crujius in a tracl: on this fubjecl:, finds fault with 
the ambiguity of " fufricient, ,, which might feem " fufficient 
for this effecV' without excluding it from the poflibility of pro- 
ducing fome other. According to him, this principle involves 
abfolute neceflity, and deftroys morality. 



LAWS OF THOUGHT. 281 

muft have a fufficient reafon why the thing or pro- 
pofition fhould be as it is and not otherwife."* 
From this law are educed fuch applications as thefe : 
— 1. Granting the reafon, we muft grant what fol- 
lows from it. On this depends fyllogiftic inference. 
2. If we reject the confequent, we muft reject the 
reafon. If we admit the confequent, we do not of 
neceffity admit the reafon. 

Now the diftinction between formal and material 
truth, or in other words between felf-confiftency in 
thinking, and conformity with facts, affifts materially 
in forming an eftimate of the worth of thefe prin- 
ciples. A judgment may be formally true, and ma- 
terially falfe ; as in the inference " No men err, 
Socrates is a man, therefore he cannot err," which 
is correctly drawn, yet proves a falfehood from a 
falfehood : or it may be materially true yet formally 
falfe, as cc Socrates is a man, Socrates erred, there- 
fore all men err;" where a true judgment has been 
drawn from two true judgments, yet not correctly. 
The four criteria in queftion are ufeful in fecuring 
formal truth, that is, in keeping our thoughts in har- 
mony with each other; but for the difcovery of 
material truth, for giving us thoughts that are true 



* Leibniz, Theod. I. § 44. Upon this principle, and thofe 
of Contradiction and Identity, Leibniz has bafed his Logic. 



282 OUTLINE OF THE 

reprefentations of fa£ts, they are either ufelefs, or only 
ufeful as principles fubordinate to the higher cri- 
terion of which all applied Logic is but the expan- 
fion, that every proportion muft reft upon fufficient 
evidence. The principle of contradiction has been 
already implied in the do£hine of privative concep- 
tions (§55) in the theory of disjunctive judgments 
and inferences (pp. 159 — 212) and in other places. 
The principle of the excluded middle is the canon of 
the inference from contradictory oppofition (p. 197) 
upon which the refutation of a falfe conclufion muft 
reft. The principle of the fufficient reafon is im- 
plied in the fyllogiftic canon (p. 214,) that every con- 
clufion muft follow from and depend on fufficient 
premiffes ; it is employed in other forms, in hypo- 
thetical reafonings in particular. And in thefe purely 
formal applications the criteria have their import- 
ance, but that not the higheft. 

Viewed as inftruments for judging of material 
truth, they fink into mere rules for the reception of 
evidence. The firft is a caution againft receiving 
into our notion of a fubjecft any attribute that is irre- 
concileable with fome other, already proved upon 
evidence we cannot doubt. The fecond is a per- 
miffion to receive attributes that are not thus mutu- 
ally oppofed, or a hint to feek for fuch only. The 
third would compel us to re-confider the evidence 



LAWS OF THOUGHT. 283 

of any propofition, when other evidence threatened 
to compel us to accept its contradictory. The fourth 
commands that we feek the caufes and laws that 
have determined the exiftence of our fubject, for the 
fubje£t cannot be adequately known except in thefe. 
So that the vaunted criteria of truth are rules of evi- 
dence -, and there is no one means of judging of 
truth, except what the whole fcience of Evidence 
affords. 

A. Construction of Science. 

§. 115. InduSf ion and Deduction. 

Indu£tion # is ufually defined to be the procefs of 
drawing a general law from a fufficient number of 
particular cafes ; deduction is the converfe procefs, 
of proving that fome property belongs to a particu- 



* Opinions are fomewhat divided both as to the meaning of 
iirayaryb, the word of which Induction is the Englifh equiva- 
lent, and the nature of the argument that bears the name. 
1. It is fuppofed to be a perfuafwe argument to which a perfon 
is induced {iirdyircti) to affent. Comp. npoc-g^s fxri <rz hrrno-ri to 
ir^ocrnylg. ahrov aal h$v ko.1 iiraywyov. (Epicletus Ench. 34.) where 
the laft word means perfuafiue, alluring. Compare Cicero (de 
Inv. I. 31.) " Induc~Ko eft oratio, quae rebus non dubiis capiat 
ajfenfiones ejus quicum inftituta eft 5 quibus afTenfionibus facit, 
ut illi dubia quaedam res, propter fimilitudinem earum rerum, 
quibus afTentit, probetur." 2. It is the bringing in (to ivkyivv) 
examples or companions, To sv rag eUovag lirayiaBeu — (Xenop/ion, 



284 OUTLINE OF THE 

lar cafe, from the confideration that it comes under a 
general law. More concifely, Induction is the pro- 
cefs of difcovering laws from fa£ts, and caufes from 
effects ; and Deduction that of deriving fa£ts from 
laws, and effects from their caufes. E. g., that 
all bodies tend to fall towards the Earth is a truth 
which has been obtained by confidering a number of 
bodies where that tendency has been difplayed, by 
induction; if from this general principle we argue 
that the ftone we throw from our hands will fhow 
the fame tendency, we deduce. If it were always 
poflible duly to examine the whole of the cafes to 
which a law applies, and to fee by intuition the figni- 



CEcon. 17 § 15.) This latter derivation finds molt favour. 
Then the procefs itfelf is fometimes defcribed as if it were a 
way of proving particular unknown facts from particular known 
facts. " Cum plura interrogaffet [Socrates], quae fateri ad- 
verfario necefle effet, noviifime id de quo quaerebatur, infere- 
bat, cui fimile concef^^Tet. ,, (J$uin8ilian, V. 11.) The logician 
will fee that this comes clofe to the logical Argument from Ex- 
ample. Both in Induction and Example, however, there is an 
appeal to a general law, expreft or implied. Our definition is 
that of Arijlotle, (Top. I. 12) " Induction is the procefs from 
particulars to univerfals. ,, In ufmg the phrafe " the fyllogifm 
from induction," A. hints at that wider view of fyllogifm, as 
the fimple element of all reafoning whatever, which it is one 
main object of this book to develope. See Heyder, Darflel- 
lung, pp. 60, 219. Ernefti Lex, Techn, Trendelenburg. Ex- 
cerpta, § 20, but chiefly Reinhardi Opufcula, I. 212. 



LAWS OF THOUGHT. 285 

ficant and important parts of each, the procefs of 
Induction would be fimple enough. But a complete 
infpe£iion of all the cafes is very feldom poflible ; 
Even the laws on whofe invariable operation the 
ftrongeft reliance is placed, muft have been laid down 
upon the evidence of a number of cafes very limited 
when compared with the whole ; that men muft all 
die, and that heavy bodies tend to fall towards the 
earth are ftatements which no one can boaft of hav- 
ing verified by enumeration. The perfect certainty 
with which they are believed, refts upon far lefs than 
the millionth part of the cafes that might be brought 
to bear witnefs about them. Nor again are the fig- 
nificant and efTential circumftances eafy to obferve, 
in the few cafes that lie within the reach. Either 
they efcape notice altogether, as did the fa£t of the 
earth's revolution in the early days of Aftronomy ; 
or they are fo entangled or overlaid with a mafs of 
other fa£ts that their importance does not at firft ap- 
pear, like the a£tion of cold in the produ£tion of 
dew, before Dr. Wells' obfervations, or the influ- 
ence of an open drain in producing and fuftaining 
fever, till within the laft few years, or (fuppofing the 
point now eftablifhed) the power of Ozone in the 
atmofphere in the complaint called Influenza, and in 
overcoming the noxious effluvia of decaying organic 
matter. It appears then that the pure indudtive fyl- 



286 OUTLINE OF THE 

logifm, that argument by which a law is laid down 
as the exact fum of all the fingle cafes, will not fuf- 
fice for fcientific refearch. To take an example — 

Gold, filver, copper and the reft will combine with oxygen, 
Gold, filver, copper and the reft are the only metals $ 
Therefore all metals combine with oxygen. 

(A fyllogifm in A U A, Fig. III. p. 236.) 

This argument could not be formed until people 
difcovered what at firft no one fufpected, that oxy- 
gen was the caufe of the rufting and tarnifhing of 
metals ; and it ftill ftands open to difpute if a metal 
fhould be hereafter difcovered that refufes to com- 
bine with oxygen. Yet it might be felected as one 
of the inductions that approaches moft near to per- 
fect enumeration. The logic of fcience then muft 
employ other inftruments than this fyllogifm, fo very 
limited in its application, fo very liable to queftion. 
Four principal queftions require to be anfwered by 
Applied Logic. 

1 . How are the caufes of fa&s to be diftinguifhed, amidft a 
multitude of other facts, all open to obfervation ? 

2. How are caufes difcovered which are lefs open to obfer- 
vation than the effects ? 

3. When fhould an incomplete enumeration (or induction) 
of facts be deemed fufficient, and on what principle ? 

4. How fhould new laws be expreffed and recorded ? 



LAWS OF THOUGHT. 287 

The following feilions contain an indication of 
the anfwers to thefe four enquiries, but by no means 
a full expofition of them. 

§ 116. Search for Caufes. Induclive Methods. 

All men are apt to notice likenefTes in the fails 
that come before them, and to group fimilar fails 
together. The fimilarities are fometimes fo obvious 
that the moft carelefs obferver is arrefted by them ; 
the rife of the tide to-day and yefterday, the tendency 
to fall which a ftone from the hand, an acorn from 
an oak, and a hailftone from a cloud exhibit alike, 
and the power of growth exhibited by a grain of corn 
and a tulip root, afford groups of cafes which feem 
fo to claffify themfelves as to leave the mind little 
room for enquiry. The faculty by which fuch fimi- 
larities are apprehended is called obfervation ; the ail 
of grouping them together under a general ftatement, 
as when we fay " All feeds grow — all bodies fall," 
has been already defcribed as generalization (p. 99). 

Now if any obvious generalization be examined, 
as for example "bodies tend to fall," we fee that this 
only furnifhes us with the fum of feveral diftinil 
fails ; that " bodies fall " is only a fhorter form of 
ftating that this body falls, and that body, and that 
other, and fo on till every fingle body has been men- 
tioned. Why all bodies tend to fall has not been 



288 OUTLINE OF THE 

ftated. In other words a law has been laid down ; 
but the caufe of its operation remains to be afcer- 
tained. A law or rule is a general principle em- 
bodying a clafs of fa£ts ; when it is regarded in its 
connexion with theory it ufually has the former 
name, and when it is concerned with practice, the 
latter. The formation of fuch general propofitions 
is the firft procedure in the formation of fcience ; at 
the fame time they are of little fervice unlefs accom- 
panied by the afcertainment of caufes. 

What then is a caufe ? It is the fum of the fa&s 
or things to which another fa£t or thing owes its 
being. The older thinkers were accuftomed to feek 
the producing or efficient caufe of anything in fome 
fingle form (caufa principalis ^ uvpiov al'riov) and to rank 
the reft of the fails which concurred to produce a 
given effe£t, in fubordinate places as inftrumental and 
impelling caufes. But it has been fliown with great 
clearnefs by Mr. J. S. Mill that this hierarchy of 
caufes leads to deceit. And we muft apply univer- 
fally, what the fcholaftic writers admitted in fome 
cafes, the principle that all the fa£ts or elements from 
which a new fa£t or thing draws its exiftence, /. e. 
all the aflbciate caufes (caufcz ejjentialiter fociatce) of 
it, make up what we term its Caufe, on the fcho- 
laftic maxim that " feveral partial caufes concurring 
for one effe£t muft be regarded as one" — {Caufce 



LAWS OF THOUGHT. 289 

partiales in toto concur fu Ji ant pro una.) The caufe 
of an explofion of coal-gas is not the lighted candle 
alone, nor the gas which it kindles, nor the admix- 
ture of common air which makes the gas explofive, 
but it is the concurrence of all three. 

Although we fay that a caufe is antecedent to its 
effedt, we muft not underftand this as implying inva- 
riable antecedence in point of time. The vices of 
the court and government caufed the French Revo- 
lution, and were antecedent to it in time ; the law of 
gravitation caufes the fall of an acorn, and concurs 
to caufe the ofcillations of a pendulum, but here the 
antecedence is that of thought only ; as the general 
precedes in thought the particular, fo does the law of 
gravitation, the bond of the univerfe, precede that 
particular form of it in v/hich a body gravitates to- 
wards our earth. It may be faid that in this ufage 
we call that an effe£t which is merely a part of the 
faft, whereas our definition of caufe requires us to 
find fome diftin£t fad:. But in truth the mind re- 
prefents the two fa£ts as diftindt ; ftones would ceafe 
to fall towards the earth if fome other body were fud- 
denly brought near enough to attract them with 
equal force in an oppofite direction, but the law of 
gravitation would ft ill hold good. So that the two 
are diftin£t, becaufe we can conceive them feparated. 
In order to conftitute any fa£t or principle the 
u 



290 OUTLINE OF THE 

caufe of other fadts, it fliould pofTefs the following 
characters.* 

A. " Invariable connexion, and, in particular, in- 
variable antecedence of the caufe and confequence 
of the effedt, unlefs prevented by fome counteracting 
caufe." 

B. " Invariable negation of the effedt with abfence 
of the caufe, unlefs fome other caufe be capable of 
producing the fame effedt." The application of 
this principle has been called the Method of Differ- 
ence. 

C. " Increafe or diminution of the efFedi, with the 
increafed or diminifhed intenfity of the caufe, in 
cafes which admit of increafe and diminution." 

D. " Proportionality of the effedt to its caufe in 
all cafes of diredt unimpeded adiion." 

E. " Reverfal of the effedt with that of the caufe." 
The application of the three laft principles confti- 
tutes the Method of Concomitant Variations. 

From thefe principles follow fome practical rules 
for afcertaining caufes ; fuch as — 

i. The caufe of a given effedt may be the fame as 
we know to produce fome fimilar effe£l in another 
cafe better known to us. 

For example, Berzelius records that a fmall bub- 

* Sir John HerfcheVs Preliminary Difcourfe, p. 151. 



LAWS OF THOUGHT. 291 

ble of the gas called feleniuretted hydrogen, infpired 
by accident through the nofe, deprived him for fome 
hours of the fenfe of fmell, and left a fevere catarrh 
which lafted for fifteen days. Dr. Prout fuggefts that 
the correfponding effects in Influenza may be trace- 
able to the fame caufe as undoubtedly produced them 
here, to the admixture namely of this or fome fimilar 
fubftance with the air we breathe ; and as a fuggef- 
tion or anticipation this is perfectly legitimate, and 
may prove highly valuable. Its inadequacy as a 
proof may be mown by throwing it into fyllogiftic 
form — 

The cafe of infpiring feleniuretted hydrogen is a cafe in which 

lofs offmell and fevere catarrh follow, 
Cafes of influenza exhibit thefe effe£ts j 
Therefore cafes of influenza are cafes in which the faid gas has 

been infpired. 

This is the mood AAA, Fig. ii. invalid becaufe 
it does not diftribute the middle term (p. 219). It 
is one of the arguments defcribed as Rhetorical En- 
thymemes below. 

2. " If in any of the facSts we have to account 
for, there be even one in which a particular charac- 
ter is wanting, that character cannot be the caufe in 
queftion ; for the true caufe can never be abfent." 

3. As the laws of nature are uniform, and never 
capricious, we are entitled to expe£l that a caufe 



292 OUTLINE OF THE 

which in feveral cafes produces a given effeft will 
always do fo ; and if it appears to be otherwife, we 
fhould either fearch for fome counteracting caufes, or 
fufpe£t the accuracy of our obfervations. 

4. " Caufes will very frequently become obvious 
by a mere arrangement of our fa£ts in the order of 
intenfity in which fome peculiar quality fubfifts : 
though not of neceflity, becaufe counteracting or 
modifying caufes may be at the fame time in action." 

" For example : found confifts in impulfes com- 
municated to our ear by the air. If a feries of im- 
pulfes of equal force be communicated to it at equal 
intervals of time, at firft in flow fucceffion, and by de- 
grees more and more rapidly, we hear at firft a rattling 
noife, then a low murmur, and then a hum, which 
by degrees acquires the character of a mufical note, 
rifing higher and higher in acutenefs, till its pitch be- 
comes too high for the ear to follow. And from this 
correfpondence between the pitch of the note and the 
rapidity of fucceffion of the impulfe, we conclude 
that our fenfation of the different pitches of mufical 
notes originates in the different rapidities with which 
thefe impulfes are communicated to our ears." To 
make fuch an arrangement, however, we muft have 
a prefage, and no uncertain one, of the caufe of our 
phenomena ; and therefore it is rather ufeful for veri- 
fication, than for fuggeftion, of a theory. 



LAWS OF THOUGHT. 293 

5. "If we can either find produced by nature, or 
produce defignedly for ourfelves, two inftances which 
agree exactly in all but one particular, and differ in 
that one, its influence in producing the phenomenon, 
if it have any, muji thereby be rendered fenfible. 
If that particular be prefent in one inftance, and 
wanting altogether in the other, the production or 
non-prod u£tion of the phenomenon will decide whe- 
ther it be or be not the only caufe : ftill more evi- 
dently, if it be prefent contrariwife in the two cafes, 
and the effedt be thereby reverfed. But if its total 
prefence or abfence only produces a change in the 
degree or intenfity of the phenomenon, we can then 
only conclude that it a£ts as a concurrent caufe or 
condition with fome other to be fought elfewhere. 
In nature, it is comparatively rare to find inftances 
pointedly differing in one circumftance and agreeing 
in every other \ but when we call experiment to our 
aid, it is eafy to produce them ; and this is, in faft, 
the grand application of experiments of enquiry in 
phyfical refearches. They become more valuable, 
and their refults clearer, in proportion as they poflefs 
this quality (of agreeing exactly in all their circum- 
ftances but one), fince the queftion put to nature be- 
comes thereby more pointed, and its anfwer more 
decifive." 

6. " Complicated phenomena, in which feveral 



294 OUTLINE OF THE 

caufes concurring, oppofing or quite independent of 
each other, operate at once, fo as to produce a com- 
pound effeft, may be Amplified by fubdu&ing the 
effect: of all the known caufes, as well as the nature 
of the cafe permits, either by dedu£tive reafoning or 
by appeal to experience, and thus leaving, as it were, 
a refidual phenomenon to be explained. It is by this 
procefs, in fa£t, that fcience, in its prefent advanced 
ftate, is chiefly promoted.'' 

" A very elegant example may be cited, from the 
explanation of the phenomena of found. The en- 
quiry into the caufe of found had led to conclufions 
refpefting its mode of propagation, from which its 
velocity in the air could be precifely calculated. 
The calculations were performed ; but, when com- 
pared with fa£t, though the agreement was quite 
fufficient to fhow the general corre£tnefs of the caufe 
and mode of propagation affigned, yet the whole ve- 
locity could not be fliown to arife from this theory. 
There was ftill a refidual velocity to be accounted 
for. At length La Place ftruck on the happy idea, 
that this might arife from the heat developed in the 
aft of that condenfation which neceffarily takes 
place at every vibration by which found is conveyed. 
The matter was fubje&ed to exa£t calculation, and 
the refult was at once the complete explanation of 
the refidual phenomenon." 

Thefe are fpecimens of the methods according to 



LAWS OF THOUGHT. 295 

which refearches into caufes are conduced. I add 
one example, combining the 4th, 5th and 6th rules, 
and exhibiting Proportionality of caufe and effecSt, 
Experiment, and Refidual Phenomena in one fet of 
enquiries. Beyond this, the limits I have prefcribed 
myfelf do not fuffer me to go. 

In Sir Humphrey Davy's experiments upon the 
decompofition of water by galvanifm, it was found 
that befides the two components of water, oxy- 
gen and hydrogen, an acid and an alkali were deve- 
loped at the two oppofite poles of the machine. As 
the theory of the analyfis of water did not give rea- 
fon to expecSt thefe products, they were a refidual 
phenomenon, the caufe of which was ftill to be found. 
Some chemifts thought that ele&ricity had the power 
of producing thefe fubftances of itfelf ; and if their 
erroneous conjecture had been adopted, fucceeding 
refearches would have gone upon a falfe fcent, confi- 
dering galvanic electricity as a producing rather than a 
decompofing force. The happier infight of Davy con- 
jedtured that there might be fome hidden caufe of this 
portion of the effecft ; the glafs veffel containing the 
water might fuffer partial decompofition, or fome fo- 
reign matter might be mingled with the water, and 
the acid and alkali be difengaged from it, fo that the 
water would have no mare in their production. Af- 
fuming this he proceeded to try whether the total re- 
moval of the caufe (B. p. 290) would deftroythe effecSt, 



296 OUTLINE OF THE 

or at leaft the diminution of it caufe a correfponding 
change in the amount of effect produced — (C. p. 
290). By the fubftitution of gold veflels for the 
glafs without any change in the effe£t, he at once 
determined that the glafs was not the caufe. Em- 
ploying diftilled water, he found a marked diminu- 
tion of the quantity of acid and alkali evolved ; ftill 
there was enough to fhow that the caufe, whatever 
it was, was ftill in operation. Impurity of the water 
then was not the fole, but a concurrent caufe. He 
now conceived that the perfpiration from the hands 
touching the inftruments, might affe£t the cafe, as it 
would contain common fait, and an acid and an alkali 
would refult from its decompofition under the agency 
of electricity . By carefully avoiding fuch contact, 
he reduced the quantity of the produ&s ftill further, 
until no more than flight traces of them were per- 
ceptible. What remained of the effect might be 
traceable to impurities of the atmofphere, decom- 
pofed by conta£t with the elecStrical apparatus. An 
experiment determined this ; the machine was placed 
under an exhaufted receiver, and when thus fecured 
from atmofpheric influence, it no longer evolved the 
acid and the alkali. 

A formal analyfis of thefe beautiful experiments 
will illuftrate the method of applying the rules of 
pure Logic in other cafes. 



LAWS OF THOUGHT. 297 

I. Statement of the cafe, the refidual caufe being ftill undif- 

covered. 
" The decompofition of water by electricity, produces oxy- 
gen and hydrogen, with an acid and an alkali." 

II. Separation of the refidual from the principal caufe. 

a. " The decompofition of water produces oxygen and hy- 

drogen. " 

b. " The production of an acid and alkali in the decompo- 

fition of water may be caufe d by action on the glafs 
veffel containing the water." (Problematical Judgment 
-A.) 

III. The latter Judgment — b — difproved by a fyllogifm in 

Mood E A O, Fig. iii. with a conclufion that contra- 

dicls it. 
" A cafe in which I employ a veffel of gold cannot involve 

any decompofmg action on a glafs veffel, 
" A cafe in which I employ a gold veffel ftill gives the acid 

and the alkali 5 
" Therefore cafes of the production of the acid and alkali 

are not always cafes in which glafs is decompofed." 

IV. Another attempt to fuggeft the refidual caufe. 

" The acid and alkali are produced by the decompofition of 
impurities in the water employed. " 

Syllogifm in A A I, Fig. iii. tending to prove this. 

" An experiment with diftilled water muft admit lefs im- 
purity, 

" An experiment with diftilled water gives lefs acid and 
alkali 5 

" Therefore fometimes with lefs impurity we have lefs acid 
and alkali. 

V. " The contact of moift hands" may be an additional caufe 

of the refidual phenomenon. 



298 OUTLINE OF THE 

Improved fyllogifm in A A I, Fig. iii. to include this con- 
current caufe. 

" An experiment with diftilled water, and apparatus kept 
from contact of hands will admity?/// lefs impurity, 

" An experiment, &c. refults in the production of ftill lefs 
acid and alkali $ 

" Therefore fometimes with ftill lefs impurity we have ftill 
lefs acid and alkali." 

VI. Amended fyllogifm. AAA, Fig. iii. 

u A cafe where we ufe thefe precautions in 'vacuo is a cafe of 

no impurity, 
" A cafe where we ufe, &c. in 'vacuo is a cafe of no acid and 

alkali 5 
" Therefore a cafe of no impurity is a cafe of no acid and 

alkali." 

VII. Immediate inference from laft conclufion. 

" Cafes of no-impurity are cafes of non -production of acid 

and alkali, 
" Therefore" (according to the example in p. 219, Divifion 

II. of inference from A) 
" All cafes of production of acid and alkali are cafes of fome 

impurity ;" 
which was to be proved. 

An example like this brings into a ftrong light 
many of the charafteriftics of inductive reafoning. 
Forms ufually confidered to be dedu£tive are here 
freely employed. The later fteps tend to confirm 
the earlier, on which, however, they themfelves de- 
pend ; fo that a mutual confirmation is obtained from 
fetting them together. When the chemift fubfti- 
tuted gold veffels for the glafs, and inferred from the 



LAWS OF THOUGHT. 299 

continuance of the effe£t under this change that the 
glafs could have nothing to do with its production, it 
was formally poffible in the then ftate of knowledge 
that the glafs might be the caufe in the one experi- 
ment, and the decompofition of the gold in the 
other. But the later fteps, which mowed that the 
effect varied with the variations in a circumftance 
wholly diftinct from the decompofition of glafs or 
gold, reduced the poffibility of maintaining fuch a 
view to the very loweft amount. Even the pre- 
miffes of particular fyllogifms in the chain are fome- 
times tefted and corrected by the conclufion, although 
formally the conclufion mould entirely depend upon 
the premhTes. The experimenter expected to find 
that the ufe of diftilled water would exclude all im- 
purity ; and he intended that his premifs (See No. 
IV.) mould affert as much; but when it turned out 
in the conclufion that the fuppofed products of the 
impurity were ftill prefent, he was reduced to the 
choice between abandoning that caufe and re-caft- 
ing his premifs fo as to admit that the caufe was 
ftill prefent — " the ufe of diftilled water gives lefs 
impurity." 

§ 117. An ticipation . 

The next queftion to be anfwered is — how are 
caufes difcovered which are not obvious, even after 
repeated infpedtion of the facts in which they lie 



300 OUTLINE OF THE 

hid ? By a power or combination of powers granted 
only to a few, which has been called Anticipation. 
It is the power of penetrating into the fecrets of na- 
ture, before the evidence is unfolded : it is enjoyed, 
as one might expert, by thofe only who have long and 
deeply ftudied the laws of nature already laid open, 
but not by all of thefe. It is no mere power of 
gueffing, but an a&ive imagination, fupplied with 
materials by a clear understanding carefully difcip- 
lined. The fyftem of anatomy which has immortal- 
ized the name of Oken, is the confequence of a flafh 
of anticipation which glanced through his mind when 
he picked up, in a chance walk, the fkull of a deer, 
bleached by the weather, and exclaimed after a glance 
" It is a vertebral column !" When Newton faw 
the apple fall, the anticipatory queftion flaftied into 
his mind, " why do not the heavenly bodies fall like 
this apple ?" In neither cafe had accident any im- 
portant fhare ; Newton and Oken were both pre- 
pared by the deepeft previous ftudy to feize upon the 
unimportant fa& offered to them, and fhow how im- 
portant it might become ; and if the apple and the 
deer's fkull had been wanting, fome other falling 
body, or fome other fkull, would have touched the 
firing fo ready to vibrate. But in each cafe there 
was a great ftep of anticipation : Oken thought he 
faw the type of the whole fkeleton in the fingle ver- 



LAWS OF THOUGHT. 301 

tebra and its modifications, whilft Newton conceived 
at once that the whole univerfe was full of bodies 
tending to fall ; two truths that can fcarcely be faid 
to be contained in the little occurrences in connec- 
tion with which they were fir ft fuggefted. 

The difcovery of Goethe, which did for the vege- 
table kingdom what Oken's did for the animal, that 
the parts of a plant are to be regarded as metamor- 
phofed leaves, is an apparent exception to the necef- 
fity of difcipline for invention, fince it was the difco- 
very of a poet in a region to which he feemed to 
have paid no efpecial or laborious attention. But 
Goethe was himfelf moft anxious to reft the bafis 
of this difcovery upon his obfervation rather than 
his imagination, and doubtlefs with good reafon.* 

A miftaken notion prevails that this rapid antici- 
pation does not belong to the philofophic caft of mind 
— that it is precifely what Bacon condemns as the 
method which " hurries on rapidly from the particu- 



* WhewelPs Hift. Sci. Ind. III. 477. As with other great 
difcoveries hints had been given already, though not purfued, 
both of Goethe's and Oken's principles. Goethe left his to 
be followed up by others, and but for his great fame, perhaps 
his name would never have been connected with it. Oken had 
amafTed all the materials neceflary for the eftablifhment of his 
theoiy ; he was able at once to difcover and conquer the new 
country. 



302 OUTLINE OF THE 

lars fupplied by the fenfes to the moft general axioms, 
and from them as principles, and their fuppofed in- 
difputable truth, derives and difcovers the interme- 
diate axioms." It is thought that caution, and 
deliberate examination of every particular we can 
find, before we allow ourfelves to form any conclu- 
sion whatever, are the conditions of all found phy- 
fical enquiry. There is here a confufion of two 
diftincSt things. Scrupulous caution ftiould be exer- 
cifed before an hypothefis is confidered to be proved; 
and the law that we believe to be true fhould be 
applied to every fa£t where it can be fuppofed to 
operate, and to every other law with which it might 
interfere, in order to verify exadHy what was at firft 
only a happy conjecture. Bacon meant to complain 
that this fober procefs did not always follow the 
bright thought and brilliant fuggeftion ; and perhaps 
that the bright thought itfelf was not fuggefted in 
the region of fadts but in that of words. When the 
ancient Aftronomy, rufhing to the general axiom 
that cc the circular motion is the moft perfeft," de- 
duced from it the intermediate axiom that the motion 
of the heavenly bodies muft be the circular, it might 
be reafonably charged with undue ufe of anticipation ; 
becaufe the higheft axiom, having no precife and de- 
finable meaning, cannot have really fprung from the 
contemplation of any fafts, nor do it and the axiom 



LAWS OF THOUGHT. 303 

drawn from it, fquare with the fails they pretend to 
embrace. Where thefe conditions are obeyed, An- 
ticipation is, as it has been called, the mother of 
fcience. " To try wrong guefles," fays Dr. Whe- 
well, " is, with moft perfons, the only way to hit 
upon right ones. The character of the true philofo- 
pher is, not that he never conjectures hazardoufly, 
but that his conjectures are clearly conceived, and 
brought into rigid contact with fails. He fees and 
compares diftinilly the ideas and the things ;— the 
relation of his notions to each other and to pheno- 
mena. Under thefe conditions, it is not only ex- 
cufable, but neceffary for him, to fnatch at every 
femblance of general rule, — to try all promifing 
forms of fimplicity and fymmetry." Anticipation 
then is the power whereby the mind prefages a truth 
before it is fairly proved, before fhe makes the at- 
tempt to efiablifh it by exail and cautious methods. 
Philofophy proceeds upon a fyftem of credit ; if fhe 
never advanced beyond her tangible capital, her 
wealth would not be fo enormous as it is. She works 
with a principle as true before (he knows it to be fo, 
becaufe in watching how it operates upon fails, con- 
fift the beft means of eftablifhing its truth ; but fhe 
muft be prepared at the fame time to abandon and 
difmifs it whenever it is found to be in direit and 
irreconcileable confliil with eflablifhed fails. 



304 OUTLINE OF THE 

§ 1 18. Induclive Conception, Colligation, Definition. . 

Upon the nature of the Conception which Antici- 
pation furnifhes, and its mare in the formation of 
fcience, much controverfy has been raifed, one party 
maintaining that the mind mull: be content with 
recording the fa£ts, and another, that a Conception 
muft anticipate the fa£ts, and furnifli us with a key- 
to their language. Granting on the one hand that 
a theory or conception to explain fa£ts will be worth - 
lefs, unlefs it (hall prove to be itfelf a fa£t, we muft 
admit on the other that great fteps of inductive dif- 
covery are made with the help of a pre-conception, 
and not by merely throwing obfervations together. 
" That the fa£t of the elliptical motion of the planet 
Mars/' fays Dr. Whewell, " was not merely the fum 
of the different obfervations, is plain from this, that 
other perfons, and Kepler himfelf before his difco- 
very, did not find it by adding together the obferva- 
tions. The fail of the elliptical orbit was not the 
fum of the obfervations merely ; it was the fum of 
the obfervations, feen under a new point of view, 
which point of view Kepler's mind fupplied." 

Such a conception, of which feveral inftances have 
now been given, effects the Colligation (to borrow 
Dr. Whewell's name) of the fa£ts to be explained. 
But in order to connect itfelf with the fa£ts, the con- 



LAWS OF THOUGHT. 305 

ception itfelf muft be capable of Explication or Defi- 
nition, not indeed of adequate definition, fince we 
mall have to alter our defcription of it from time to 
time with the advance of knowledge, but ftill capa- 
ble of a precife and clear explanation. For example 
a large clafs of fa£r.s is bound together by the notion 
of " chemical affinity," and could not be underftood 
and arranged without the thread of this Conception 
to run through them. To refer them to this, their 
proper Conception, is one operation; to give a proper 
Explanation of chemical affinity another. 

Definition. — Chemical affinity is the power by which the 
particles of one elementary body are made to cohere 
with thofe of another, fo as to produce a new mbftance. 
with characters either diftincl: from or oppofed to thofe 
of the conftituents feparately. 

Proposition. — The tarnifhing of metals, the neutral fairs, 
&c. &c. are inftances of the action of chemical affinity. 

Therefore we expect to find in them the characters mentioned 
in the definition. 

This is a fyllogifm in U A A, Fig. 1 ; and whilft 
our reafoning faculty can draw it out and appreciate 
its truth and applicability, reafon alone could not 
have fuggefted the premifTes. No rules can be given 
for the difcovery of the appropriate conception that 
explains our facts ; "fuch events," fays Dr. Whewell, 
" appear to refult from a peculiar fagacity and felicity 
of mind — never without labour — never without pre- 

x 



306 OUTLINE OF THE 

paration ; yet with no conftant dependence upon 
preparation, upon labour, or even entirely upon per- 
fonal endowments." The fuggeftion of the concep- 
tion may be due almoft entirely to accident ; the 
explication of it, often by far the more difficult ftep, 
cannot be accidental, but will proceed from a natural 
fagacity highly difciplined by fcientific purfuits. 

Conceptions not wholly correct: may ferve for a 
time for the Colligation of Fafts, and may guide us 
in refearches which mail end in a more exadt Colli- 
gation. The theory of circular motions of the hea- 
venly bodies was of this kind; and in its turn the con- 
ception of epicycles. The theory of Phlogifton in 
chemiftry made many fa£ts intelligible ; before the 
correfter one of Oxidation fuperfeded it. So with 
the theory of " Nature abhors a vacuum," which 
ferved to bring together many cognate fa£ts, not pre- 
vioufly confidered as related. Any incorreft concep- 
tion of this kind has a place in fcience, whilft and in 
fo far as it is applicable to fa£ts and renders them intel- 
ligible. As foon as fadts occur which it is inadequate 
to explain, we either correct, or replace it by a new 
one. 

§ 119. Complete and Incomplete Induclion. 

The third queftion that demanded an anfwer was 
—on what principle are incomplete indudtions, u e. 



LAWS OF THOUGHT. 307 

examinations of fa&s that flop fbort of complete 
enumeration, fufficient to eftablifh general laws ? 
The anfwer will contain the mod interefting and im- 
portant of the principles of Logic. All our expe- 
rience teaches us that in the univerfe, the "Cofmos," 
whofe very name means order, regularity and uni- 
formity prevail, and caprice and uncertainty are ex- 
cluded. Whilft it is conceivable that any one of the 
natural laws in which we place moft confidence 
might be reverfed, whilft it is certain that many of 
them have been miraculoufly fufpended for purpofes 
proportion ably great and important, our prefent be- 
lief in their permanence is almoft unlimited. The 
thought that there might be no more daylight, if our 
planet ceafed to revolve whilft one fide of it was 
averted from the fun — that a draught from the fpring 
would to-day deftroy the life which it recruited yef- 
terday — that a ftone thrown from the hand would 
remain fufpended in mid-air inftead of falling — never 
enters our minds, except perhaps as an amufing fancy ; 
yet each of thefe things is formally poffible. Our 
confidence in the uniformity of natural laws is em- 
bodied in the Canon, that under the fame circum- 
Jiances and with the fame fubjiances the fame effects 
always refult from the fame caufes. This great in- 
ductive principle is itfelf proved by induction, and 
partakes of the fame formal defedt that may be 



308 OUTLINE OF THE 

charged againft other inductive refults, viz. that its 
terms are wider than our experience can warrant. 
Many groups of fa£ts, conne£ted as caufes and ef- 
fefts, have not been examined; and in them it is 
conceivable at leaft that there may be capricious 
caufes producing oppofite effefts at different times. 
If this were otherwife — if the canon were the refult 
of a fimple enumeration of all poflible cafes, its pre- 
fent value as a rule would difappear; fince it is to 
unknown and unexamined cafes that we chiefly wifh 
to apply it. We draw a univerfal canon from an 
experience lefs than univerfal, and then employ it to 
juftify us in drawing other univerfal truths from other 
particular experiences . 

The difficulty, however, in applying this Canon is 
to difcover the exiftence of a law of nature in any 
fet of fafts, and how far the interference of other 
laws permit it to operate. And here the relation be- 
tween Deduction and Indu£tion, between Synthefis 
and Analyfis, is of great fervice. Thefe pairs of 
terms correfpond exaftly, as names for the fame two 
procefles ; but Induction and Deduction give promi- 
nence to the law, Analyfis and Synthefis to the fa£t. 
Thus we call the law of gravitation an induftive law, 
and fpeak of deductions from it, thinking more in 
both cafes of the univerfal than of the particular 
cafes it referred to. But we analyfe a fa£t or a fub- 



LAWS OF THOUGHT. 309 

ftance, and make a fynthefis (or placing together of 
elements) to reproduce the fa£t or fubftance. Ufing 
the two former names, the univerfal, the law, the 
world of conception, the abftradt is made promi- 
nent ; ufing the two latter, we give prominence to 
the fingle cafe, the phenomenon, the world of the 
fenfes, the concrete. The fuppofed general principle 
may be tried by applying it to a new particular cafe, 
the analyfis of a fa£t into its elements may be tefted 
by putting the elements together anew, and feeing if 
the fa£t is reproduced, the corre£tnefs of the obferva- 
tions may be confirmed by careful experiment. And 
fuch attempts offer a twofold advantage. If, on apply- 
ing fome general principle of which we are ftill uncer- 
tain, to a new particular cafe, we find that it helps to 
explain the particular, this is one fruit of the procefs ; 
and another is that our confidence in the general prin- 
ciple is materially ftrengthened. Law explains fa£t ; 
fa£t confirms law. And after this alternate afcent 
and defcent has been a few times performed, our be- 
lief in the corre£tnefs of its refults is quite complete. 
This procefs can be underftood moft readily from 
examples. The metal called Potaflium was difco- 
vered in a£r.ing on potafh by the voltaic battery \ and 
thus far the two judgments 

Potafh is an alkali, 
Potafh yields Potaflium ; 



3io OUTLINE OF THE 

would feem fufficient to defcribe the refult. But 
not fo ; a mind difciplined to fcientific enquiry, faw 
at once that this fingle fa£t was an indication of a 
law. In the fyftem of nature is no caprice ; if the 
power of yielding a metal belonged to this alkali as 
fuch^ beyond doubt other alkalies would participate 
in it. Thefe two judgments therefore become pre- 
mises to an aft of indu6tive reafoning. 

(A A A, Fig. in.) 

Potafh yields a metal, 

Potafh is an alkali ; 

Therefore all alkalies contain a metal. 

Now this fyllogifm is formally incorreft, for we 
cannot argue from a fingle alkali to the whole, and 
the property we have difcovered may belong to this 
alone in connexion with fome undifcovered peculi- 
arity. How fhall this be afcertained ? By trying 
how the conclufion, upon which fufpicion refts, will 
apply to new cafes ; by experimenting on another 
alkali as if the univerfal law were already eftablifhed, 
by deducing from it, as we have induced to it. 

(A A A, Fig. i.) 

All alkalies contain a metal, 

Soda is an alkali ; 

Therefore it rauft contain a metal. 

The experiment is tried, and anfwers perfe&ly. 



LAWS OF THOUGHT. 311 

And the fuccefs of the prediction operates ftrongly 
to raife our belief in the conclufion, on which it pro- 
ceeded. That alkalies in general have a metallic 
bafe, was indicated at firft by one cafe alone, that of 
potafh \ but the chemift was guided by that cafe to a 
fecond attempt, and now a fecond one ftrengthens 
his belief that a law exifts. To extend the trials to 
the alkaline earths, is fuggefted by their fimilarity to 
alkalies \ with them too the experiments are fuccefT- 
ful, and the law is confidered to be eftablifhed. And 
though ammonia furnifhes an apparent exception, as 
it has been found impoffible from the volatile nature 
of that fubftance to procure ammonium from it, I 
fuppofe that no fkilful chemift doubts that ammonium 
exifts, fo ftrong is the general conviction that na- 
ture's laws are uniform, and that where moft fub- 
ftances alike in their general character exhibit fome 
ftriking property, it has been granted to them all 
without exception. 

Two principles then are eftablifhed, that the cor- 
reftnefs of fynthefis is proportionate to that of the 
preceding analyfis ; and that a doubtful analyfis may 
be confirmed by a fynthefis. In other words, a cor- 
re£t induction furnifhes the premifs for a found de- 
duction, and a doubtful induCtion muft be verified 
by deductions from it. Examples of thefe may be 
found on every fide. The artillery-man, when he 



312 OUTLINE OF THE 

points a gun according to known rules, executes a 
fynthefis of feveral principles, the law of gravitation, 
that of momentum, that of atmofpheric refiftance ; 
if his fliot mifles, it will be either becaufe fome ele- 
ment has been left out of the analyfis, the compara- 
tive force perhaps of different forts of powder, and 
the windage of a loofe ball in the barrd'of the piece; 
or becaufe the influence of each of the known laws 
has not been duly apportioned. The theory that 
marble is carbonate of lime fufed under prefTure has 
been made highly probable by the (fynthetic) experi- 
ments of Sir James Hall, who made a fubftance 
clofely refembling marble by thofe means. A corre£t 
analyfis of lapis lazuli was fufpedtedto be erroneous, 
becaufe there feemed to be nothing in the elements 
affigned it, which were filica, alumina, foda, fulphur, 
and a trace of iron, to account for the brilliant blue 
colour of the ftone ; accidental fynthefis, which was 
followed up by intentional, reproduced it, and thus 
the analyfis was found to be correct, whilft the fyn- 
thefis is now daily performed for commercial purpofes. 
The law that the planets are retained in their orbits 
by an attractive force that varies inverfely as the fquare 
of their diftance from the fun has been worked out to 
its theoretical refults, and thefe have been compared, 
fynthetically, with the known facts. Theory was 
found not to correfpond with fait in all refpe£ts, and 



LAWS OF THOUGHT. 313 

thus it became neceflary to revife the analyfis, and 
difcover the refidual caufes that produced the varia- 
tion ; which aftronomers have fucceeded in doing. 

By the mutual co-operation then of thefe two pro- 
cefTes, the phyfical fciences are advanced.* If no 
attempts were made to draw a conclufion and fee 
what ufe could be made of it, till grounds formally 
complete were before us, conclufions would never be 
drawn. The certainties by which the chemift, the 
aftronomer, the geologift conduits his operations with 
compofure and fuccefs, were once bare poffibilities, 
which after being handed back and forward between 
Induction and Deduction, turned out to be truths. 
This leads on to other confiderations, firft as to the 
Modality of Judgments, that is, the degree of our 
belief in them, and next as to the ufe of the Syllogifm 
in the procedure juft defcribed. 



* Table of the relation of thefe procejfes. 


By Deduction 


By Induction 


or Synthefis 


or Analyfis 


in Teaching 


in Learning 


or Verification 


or Invention 


or yma-iq {Ar.) 


or evpsvts (Ar.) 


we pi 


oceed from 


Law 


Fa& 


Rule 


Example 


Caufe 


Effeft 


»t ( {Ar.) 


on (Ar.) 


^0 t5v app^Sv (Ar 


.) Itt; raj a?X*$' (^ r 



314 OUTLINE OF THE 

§ 120. Beliefs and degrees of Belief \ 

In forming any judgment we cannot avoid attach- 
ing to it a particular degree of credence, which might 
be, and often is, expreffed by the infertion of fome 
adverb to qualify the copula ; thus " To-morrow will 
(poffibly) be fine," and "Two ftraight lines (indif- 
putably) cannot enclofe a fpace." Although one of 
thefe judgments admits a degree of doubt, which the 
other excludes, the difference lies in our knowledge 
of the things fpoken of, rather than in the things 
themfelves. To-morrow v/ill be fine or will be 
ftormy, and it is fixed by the laws of nature which 
fhall happen ; but to us the matter is purely doubtful, 
becaufe we cannot fee into the order of nature as to 
this particular. Doubtful ftatements may become 
certain, without any alteration in the fafts to which 
they relate, by changes in our knowledge. A child 
fees with wonder a lunar eclipfe, and thinks that 
pojfibly another may happen to-morrow ; when he has 
learnt Aftronomy he may be able to fay from exaft 
calculations, upon what day one may pofitively be 
expe£led. Yet here the order of things remains the 
fame. The amount of belief which we have in our 
judgment has been called its Modality, as being the 
mode in which we hold it for truth. Arranging the 
degrees of Modality in an afcending fcale, we find 
that a judgment may be 



LAWS OF THOUGHT. 315 

1 . Poffible, where upon the firft view we have no 
caufe to think that the predicate may not be truly 
faid of the fubjecT:, but have not examined. Does 
this amount to a judgment ? or is it the ftep which 
muft precede the formation of the weakeft kind of 
judgment ? 

2. Doubtful, where we have tefted it in fome 
cafes, and found that fome feem to confirm it, whilft 
fome are doubtful. 

3. Probable, where all the trials we have made 
are favourable, but the number of them is not fuf- 
ficient to warrant certainty. 

4. Morally certain for the thinker himfelf ; where 
from examination of the matter, or prejudice, or in- 
tereft, he has formed his own belief, but cannot put 
forward fufficient grounds for it, fo as to control that 
of others. 

5. Morally certain for a clafs or fchool ; where 
the judgment refts upon grounds which are fufficient 
for all men of the fame habits of thought, or the 
fame education as the thinker. 

6. Morally certain for all ; as for example the 
belief that there is a future ftate, which though not 
abfolutely demonftrable, refts upon fuch grounds that 
it ought to influence the conduit [mores) of every 
man. 

7. Phyfically certain, with a limit; where the 
judgment is grounded on an induction fuppofed to 



316 OUTLINE OF THE 

be complete, but with the poffibility that future in- 
duction may fuperfede it. 

8. Phyfically certain without limitation ; as our 
belief in the law of gravitation, the law of chemical 
affinity, &c. 

9. Mathematically certain; where doubt cannot 
be admitted. Ex. gr. the axiom — Two ftraight 
lines cannot enclofe a fpace, or the theorem — The 
angles at the bafe of an ifofceles triangle are equal. 

All thefe degrees of belief may, upon a broader 
principle of divifion, be refolved into three. 

Our judgments, according to Ariftotle, are either 
problematical, affertive^ or demonstrable ; or in other 
words, the refiilts of Opinion, of Belief, or of Science. 

The problematical judgment is neither fubjedtively 
nor objectively true, that is, it is neither held with 
entire certainty by the thinking fubjecSt, nor can we 
mow that it truly reprefents the object about which 
we judge. It is a mere opinion. It may however 
be the expreffion of our prefentiment of certainty ; 
and what was held as mere opinion before proof, may 
afterwards be proved to demonftration. Great dis- 
coveries are problems at firft, and the examination of 
them leads to a conviction of their truth, as it has 
done to the abandonment of many falfe opinions. 
In other fubjeCts we cannot from the nature of the 
cafe advance beyond mere opinion. Whenever we 



LAWS OF THOUGHT. 317 

judge about variable things, as the future actions of 
men, the beft courfe of conduct for ourfelves under 
doubtful circumftances, hiftorical facts about which 
there is conflicting teftimony, we can but form a 
problematical judgment, and muft admit the poffi- 
bility of error at the moment of making our decifion. 

The afTertive judgment is one of which we are 
fully perfuaded ourfelves, but cannot give grounds for 
our belief, that fhall compel men in general to coin- 
cide with us. It is therefore fubjectively, but not 
objectively certain. It commends itfelf to our moral 
nature, and in fo far as other men are of the fame 
difpofition, they will accept it likewife. 

The demonftrative judgment is both fubjectively 
and objectively true. It may either be certain in 
itfelf, as a mathematical axiom is, or capable of proof 
by means of other judgments, as the theorems of 
mathematics and the laws of phyfical fcience. 

§ 121. The Syllogifm both deduSflve and induSfive. 

It is a great misfortune for Logic that the Syllo- 
gifm has been regarded as an inftrument for deduc- 
tion only. An error of Ariftotle's, for the correction 
of which his many-fided mind has itfelf fupplied 
hints, has been tenacioufly preferved ; and according 
to it, four modes of fyllogifm, in which we ftart from 
a general law as our main premifs, have been re- 



318 OUTLINE OF THE 

garded as the only perfe£t forms, and opinions have 
been pronounced upon the whole fyllogiftic fyftem 
from thefe four fpecimens. We need not wonder 
then that modes only adapted for teaching truth, have 
been pronounced ufelefs for difcovering it ; that when 
dedu£live arguments are fele£ted, it fhould be eafy 
to prove that they will not do the work of indu&ive. 
But it is wonderful that fo few fliould have perceived 
how abfurd were the attempts to turn the fo-called 
imperfeft modes into perfe£t ones. It has been 
fliown already (p. 227), that the modes of each figure 
in the old arrangement had their proper ufe, that the 
firft ferved for deducing fa£ts from laws, the fecond 
for eftablifhing differences, and the third for bringing 
in examples and exceptions. Yet logicians have 
perfifted in torturing fyllogifms of the fecond and 
third figures into the firft, by the help of Converfion, 
without perceiving that they turned a natural argu- 
ment into a diftorted monfter. To fay— 

(A A I, Fig. in.) 

Lead is fufible, 

Lead is a metal 3 

Therefore fome metal is fuflble : — 

is natural enough ; but it partakes far more of the 
nature of induction than deduction, becaufe it is ad- 
vancing from a fingle obfervation towards a more 
general ftatement, which may end probably in a uni- 



LAWS OF THOUGHT. 319 

verfal. Now to eftablifh the erroneous affertion that 
all fyllogifms are deductions, logicians are bound 
either to deny that fuch an argument is a fyllogifm, 
or to attempt to reduce it to one of the deductive 
modes. They adopt the latter alternative, thus — 

(All, Fig. 1.) 

Lead is fufible, 
Some metal is lead 5 
Therefore fome metal is fufible. 

But this unnatural form is no more like deduction 
than before j there is no reafoning from a law to facts, 
from a general to a particular ftatement, and all that 
has been done is to give us for a fecond premifs an 
unnatural judgment fuch as logicians have taught us 
already to avoid as much as poffible (p. 177). 

The fyllogifm is not confined to deductive argu- 
ments. Every one of the inductive methods already 
defcribed, falls eafily into an appropriate fyllogiftic 
form ; and we can no more reafon without making 
fyllogifms than we can fpeak and argue without form- 
ing fentences. What Grammar does for fpeech Lo- 
gic does for thought ; it afcertains its fimple elements 
and exhibits them, and if it be found that the induc- 
tive proceffes do not fall readily under the old forms, 
it would be right to confider fir ft whether the forms 
could be amended and enlarged, rather than to aban- 
don at once one half the territory of thought, the 



320 OUTLINE OF THE 

whole of which Logic has always by its names and 
definitions feemed to claim. 

To affign one half the domain of Logic to Induc- 
tion is not ftri£tly correct. There is in truth a third 
procefs, of fome fubordinate advantage in inveftiga- 
tion, whereby no advance is made towards general 
Jaws, as in Induction, nor towards the application of 
laws to fafts, as in Dedu&ion, but the matter of 
knowledge is exhibited under a new and more con- 
venient form. It would be appropriately named 
Traduction. The modes U U U in all the figures 
exemplify it moft perfe&ly; but whenever we define 
a term, or divide it, or fubftitute another for it (p. 
156J, in a word whenever we form a univerfal fubfti- 
tutive judgment, we adopt this method, of exhibiting 
old matter under a new form, without advancing 
higher towards new clafTes, or lower towards new 
fpecial applications and examples \ and therefore every 
mode containing a U judgment partakes of the tra- 
duftive procefs. 

§ 122. Employment of defeSfive Syllogifms. 

The difficulty in anfwering the queftion — how 
does Logic aid by the fyllogifm in adding to our 
itock of knowledge ? has been caufed principally bv 
ftudying only the complete forms of fyllogifm, whereas 
in difcovery it is necefTary to accept defective forms, 



LAWS OF THOUGHT. 321 

only fufpending our adoption of them until they are 
fortified by other evidence. The fact that fuch fuf- 
penfe is necefTary proves that the forms are imper- 
fect \ the fa£t that we have attained new truths from 
evidence formally infufficient to eftablifh them by 
itfelf, proves their ufefulnefs. This will appear from 
a defcription of fome of the befl known forms of 
defective fyllogifm. 

The Rhetorical Enthymeme as defcribed by 
Ariftotle, is " a fyllogifm from probable propofitions 
or from figns." The probable propofition (sUog) is 
that fort of ftatement which muft fatisfy us in mat- 
ters where univerfal affertions are impoffible ; as in 
human affairs, that " injured men will feek revenge 
— men are active where their intereft is concerned/' 
and the like. Any fyllogifm into which a propofition 
of this fort, general but by no means univerfal, enters, 
can only fupply a general and therefore uncertain 
conclufion. The fign [crn^ziov) according to Ariftotle, 
is a propofition in which fome one fait or mark that 
accompanies, precedes or follows, another fail or 
conception, is adduced as a necefTary or probable 
indication that the other is prefent. (Pri. An. ii. 27.) 
In defcribing a fign as " a propofition," fome vio- 
lence is done to language, fince it can always be 
exprefled as a fingle term. As no account is taken 
of negative figns, indications, that is, that a given 

y 



322 OUTLINE OF THE 

thing does not exift, all the Enthymemes bafed on 
figns will be pofitive or affirmative ; and as they are 
to prove the exiftence of a given fa£t without limita- 
tion, their conclufions will alfo be univerfal. Now 
fome of them are found to furnifh demonftrative 
proof of the point they would eftablifti ; and thefe 
are called Proofs. Others only afford a prefumption 
more or lefs valid that the conclufion is true. This 
difference becomes manifeft from the ufe of the three 
Figures ; the Proofs will only be found, where the 
mode and figure of the fyllogifm, made out of the 
terms of the queftion with the fign for a middle term, 
are logically valid. Where they are invalid, the fign 
will fall fhort of a Proof to the extent of that inva- 
lidity. Thus, of three Enthymemes ; (i.) Dionyfius 
muft fear, becaufe he is a tyrant ; (n.) This man is 
the murderer, becaufe he was near the murdered man ; 
(in.) As we fee from the cafe of Lord Bacon, con- 
templative men are competent to the affairs of life ; — 
each falls into a different figure. 



(I. AAA.) 

All tyrants fear, 
Dionyfius is a tyrant 5 
He muft fear. 



(II. AAA.) 

The murderer would be near, 
This man is near $ 
, He is the murderer. 



(III. A A A.) 
Lord Bacon was a practical man, 
Lord Bacon was contemplative 5 
1 All contemplative men are fit for practical life. 



LAWS OF THOUGHT. 323 

Of thefe the firft alone is formally conclufive, be- 
caufe it violates no fyllogiftic rule ; it amounts there- 
fore to a fcientific proof. Not fo the fecond ; it has 
not diflributed the middle term (p. 219), it mould 
have mown not only that the murderer muft be near, 
but that he alone could be fo. The third again 
draws a conclufion far too wide for its premifles ; 
what is true of Lord Bacon need not be fo of the 
whole clafs from which he has been fele£ted. On 
reference to the table (p. 236) it will be found that 
A A A is omitted both from the fecond and third 
Figures, in confequence of thefe defects. But are 
thefe imperfect modes quite ufelefs ? Far from it. 
A fingle argument of this kind eftablifhes a prefump- 
tion of agreement between the terms of the conclu- 
fion, and inftigates to the fearch for other confirma- 
tory figns. But feveral concurrent Enthymemes are 
often as cogent as a demonftrative fyllogifm. In the 
inveftigation of the authorfhip of the letters of Ju- 
nius, Mr. Taylor employs of neceffity a firing of 
enthymemes in the fecond Figure, each in itfelf de- 
fective, but all together forming a very ftrong cafe. 
Thus, 

The author of " Junius" wrote a particular hand, 

Sir Philip Francis wrote the fame kind of hand ; 

Therefore Sir Philip Francis is the author of " Junius." 

The author of " Junius" made certain miftakes in correct- 
ing proof-fheets, 



324 OUTLINE OF THE 

Sir Philip Francis made the fame miftakes ; 
Therefore Sir Philip Francis is the author of " Junius." 

The author of "Junius" had a particular ftyle, 

Sir Philip Francis wrote the fame ftyle ; 

Therefore Sir Philip Francis is the author of "Junius." 

The author of " Junius" is guilty of an anomalous ufe of 

certain words, 
Sir Philip Francis is guilty of the fame ; 
Therefore Sir Philip Francis is the author of "Junius. " 

The author of "Junius" employs certain images, 

Sir Philip Francis employs the fame ; 

Therefore Sir Philip Francis is the author of " Junius." 

The author of" Junius" ceafed to write at a particular time, 
Sir Philip Francis muft have ceafed to write at the fame time 5 
Therefore Sir Philip Francis is the author of " Junius." 

The refults of thefe and feveral fimilar arguments 
are fummed up in a fyllogifm which moft people, un- 
lefs they could affail the truth of feme of the ftate- 
ments, would think conclufive, to the effedt that 
two perfons who in fo many points are not found to 
differ muft be one and the fame. Circumftantial 
evidence falls naturally into a feries of Enthymemes 
of the fecond figure. Thofe of the third figure are 
employed in indudHve reafoning ; and a feries of them 
might afford a very high degree of probability that 
the conclufion common to all was true. Ariftotle's 
do6lrine of Enthymemes differs from the ordinary 



LAWS OF THOUGHT. 325 

view of fyllogifm, only as to the order of ftatement 
of thefe as diftinguifhed from common fyllogifms, 
and the licenfe allowed to employ provifionally, de- 
fective arguments, where better cannot be found. In 
any fyllogifm whatever, if we regard the queftion or 
conclufion firft, as Ariftotle does in this cafe, we 
may call the middle term a fign of its truth : but it is 
an important admiffion that figns may be ufed which 
do not prove the queftion, and only eftablifh a pre- 
emption ftronger or weaker in its favour. 

The Example is an argument which proves 
fomething to be true in a particular cafe from ano- 
ther particular cafe. Thus " Harvey might expert 
to be perfecuted for his difcovery of the circulation 
of the blood, becaufe Galileo was for his difcovery." 
But the connexion between two diftin6t fa£ts can 
only depend upon their coming under fome common 
law, and therefore in the Example the proof is not 
of one particular judgment by another, but of a par- 
ticular by means of a univerfal, for which another 
particular is the fign. Thus 

(Enthymeme in AAA, Fig. in. with Epifyllogifm 
in A A A, Fig. i.) 

Galileo was perfecuted, 

Galileo was a difcoverer in fcience ; 

Therefore all difcoverers are likely to be perfecuted. 

Harvey is a difcoverer, 

Therefore he too will be perfecuted. 



326 OUTLINE OF THE 

This argument is called " rhetorical indu&ion ;" it 
differs from induction proper in bringing in only one 
example inftead of many, and in going on to prove 
another particular cafe, inftead of flopping at the 
general law. # The flaw in it is obvious ; but the 
nearer the predicate of the fecond premifs approaches 
to diftribution, the lefs probable is an error. If it 
could be fhown that " Galileo was a fair fample of 
all difcoverers," the mode would become A U A 
Fig. in. which is formally corre£t. But in its 
weaker form it is perpetually employed. 

The Induction by Imperfect Enumeration 
is an argument which eftablifhes a general law or rule 
from a number of examples of it lefs than the whole. 
Thus 

(In AAA. Fig. m.) 

Gold, filver, and copper melt, 

They are metals 5 

Therefore all metals will melt. 

Its formal fault is the fame as that of the Enthy- 
meme of the 3rd Figure (p. 322), with which it is 
almoft identical : the conditions on which it may be 
employed have been explained above. 

* This difference difappears if with Diogenes Laertius, and 
Cicero, we defcribe Induction as an argument from particu- 
lars to like particulars. Heyder, Darftellung, p. 60. 



LAWS OF THOUGHT. 327 

§ 123. Syllogifms of Analogy. 

Analogy has been defined " The fimilarity of ratios 
or relations ;" and as each relation fuppofes two cog- 
nate things, a comparifon of relations would imply 
four things, and four terms to exprefs them. Thus 
(to employ one of Archbiftiop Whateley's examples) 
when Mandeville ufes as an argument againfl: popu- 
lar education, that, "If the horfe knew enough he 
would foon throw his rider," he intends to imply two 
pairs of related terms — 

As the horfe is to its rider, fo is the people to its rulers — 

and to aflfert further that fince the one relation de- 
depends upon the continuance of ignorance on the 
part of the horfe, the other depends upon ignorance 
alfo. Common fenfe fuggefts the refutation of fuch 
an argument ; we deny that the relations are fimilar, 
or at leaft that the fimilarity reaches fo far as to war- 
rant fuch an affertion as is founded upon it. Simi- 
larity of relations may exift however where there is 
no refemblance between the related things. 

But in popular language we extend the word ana- 
logy to include refemblances of things, as well as of 
relations. Analogy in this fenfe has exercifed an 
immenfe influence on the formation of language. In 
innumerable cafes vifible or tangible things lend their 



328 OUTLINE OF THE 

names to invifible and fpiritual, from a refemblance 
more or lefs ftriking between them. TranfgreJJion 
in its primary fenfe means the croffing over a vifible 
boundary \ right means ftraight, and wrong means 
twilled. We fpeak of a clear ftatement, a lofty 
mind, and a deep thought, all thefe adjectives being 
drawn from the analogies of the material world. 
Whilft we can exhibit them in the form of a ftate- 
ment of proportions, fo as to vindicate the original 
fenfe of analogy, it is not neceflary, nor in all cafes 
natural, to do fo. We may confider therefore that 
fimilarity of attributes, as well as of relations, may 
have the name of analogy. 

Employed as an argument, analogy depends upon 
the canon — the fame attributes may be ajfigned to dif- 
tincl but fimilar things, provided they can be Jbown to 
accompany the points of refemblance in the things, and 
not the points of difference. But fmce the pre-fuppo- 
fition of a power of difcerning to what part of the 
things the attributes belong, is indifpenfable, the ar- 
gument itfelf depends for its weight upon fomething 
external to itfelf, and finks into a mere expolition. 
In a fyllogifm proving that the metropolis, as the 
heart of a ftate, fhould not be fuffered to become too 
large, becaufe a large heart is difeafed, the real dis- 
pute would not be about the fyllogifm itfelf — 



LAWS OF THOUGHT. 329 

The heart in relation to the body mould not be too large,. 
The heart in relation to the body = (partly) the metropolis 

in relation to the ftate $ 
Therefore the metropolis to the ftate mould not be too large. 

This inference (in E U E, Fig. in.) is faultlefs, 
provided we admit that the partial identity eftablifhed 
between the heart and the metropolis includes the 
point of fize ; and to decide this, other arguments 
will be requifite, which, if unfuccefsful, will render 
the prefent one falfe, if fuccefsful, needlefs. And 
therefore arguments of this kind, founded on a ques- 
tionable refemblance, are ufed rather to fuggeft com- 
parifons, and fo perfuade, than to compel conviction ; 
and philofophers have had great caufe to complain of 
the many fallacies which become current through 
falfe "metaphorical analogies. " 

But where the refemblance between two things is 
undoubted, and does not depend on one or two ex- 
ternal features, analogy tends much more ftrongly 
to perfuafion at leaft,' though it cannot amount to 
demonftration. Its principle would be — When one 
thing refembles another in known particulars , it will re- 
femble it alfo in the unknown. The expreffion of their 
agreement muft be a qualified judgment of identity — 
a U. They muft not be of the fame kind, but only 
of a fimilar one, otherwife the argument is a mere 
cafe of Example. Neither muft the ufual tefts have 



330 OUTLINE OF THE 

been applied (fee p. 290) to prove that the known 
particulars invariably accompany the unknown, other- 
wife, as Mr. Mill obferves, we trench upon the 
ground of Induction. In venturing thus to affign 
attributes to a thing, becaufe other things of a differ- 
ent clafs have them, we fhow our dependence on the 
regularity and confiftency of creation. When the 
geologift difcovers a foffil animal with large ftrong 
blunt claws, he infers that it procured its food by 
fcratching or burrowing in the earth, trufting that a 
conformation which in other kinds of animals ac- 
companies this particular mode of life, would not be 
arbitrarily and exceptionally affigned in this cafe to 
an animal of difFerent purfuits. The following ex- 
ample, from Bifhop Butler, of a falfe analogy, and its 
refutation, will fhow the fyllogiftic treatment of ana- 
logies : — 

" There is little prefumption that death is the deftruclion 
of human creatures. However there is the fhadow of an ana- 
logy, which may lead us to imagine it is — the fuppofed likenefs 
which is obferved between the decay of vegetables and of liv- 
ing creatures. And this likenefs is indeed fufficient to afford 
the poets very apt allufions to the flowers of the field, in their 
pictures of the frailty of our prefent life. But, in reafon, the 
analogy is fo far from holding, that there appears no ground 
even for the comparifon, as to the prefent queftion ; becaufe one 
of the two fubje6ls compared is wholly void of that which is 
the principal and chief thing in the other, the power of per- 
ception and of aclion 5 and which is the only thing we are en- 



LAWS OF THOUGHT. 331 

quiring about the continuance of. So that the deftru&ion of a 
vegetable is an event not fimilar, or analogous, to the deftruc- 
tion of a living agent. " 

This may be refolved into two fyllogifms. 

I. Analogy— in A U A, Fig. in. 
The decay of vegetables is total deftru£Kon, 
The decay of vegetables zz (for prefent purpofes) the decay 

of living creatures 5 
Therefore the decay of living creatures is total deftruclion. 

II. Refutation — in AEE, Fig. 11. 

The decay of animals is that of living acting creatures, 
The decay of vegetables is not that of living acting creatures 5 
Therefore the decay of vegetables is not the fame as that of 
animals. 

The conclufion E of the latter fyllogifm is oppofed 
as a contrary (p. 197) to the premifs U of the former. 



§ 124. Syllogifms of Chance, 

Chance # may be defcribed as the amount of be- 
lief with which we expect one or other, out of two 

* The materials of this feclion are taken entirely from 
Quetelet on Probabilities (of which moft interefling work 
there is a readable and fpirited translation by Mr. G. O. 
Dowunes), and from the Formal Logic of ProferTor De Morgan, 
whofe refearches, there, in the Cambridge Philof. Tranf. and 
in the Encyclopaedia Metrop. are fpoken of by thofe better 
able to follow them than myfelf, as very acute and profound. 
ProfefTor Donkin (Philof. Mag. May, 18 51) has developed 



332 OUTLINE OF THE 

or more uncertain events. Uncertain events are 
thofe wherein no caufe or law appears, to determine 
the occurrence of one rather than of another. As 
all queftions into which this notion enters demand a 
numerical ftatement, the do&rine of Chances is 
ufually regarded as a branch of mathematics ; and 
its intricacies can only be explained by perfons 
deeply converfant with that fcience, who have 
turned their attention to this fpecial branch of en- 
quiry. Only the bare elements of it can be given 
here, with a few of the fimpleft examples. 

I. The firft principle is that the probability of an 
uncertain event is reprefented by the number of chances 
favourable to an event divided by the total number of 
chances. Thus the chances that a pictured card 
will be drawn out of a pack at random, the firft at- 
tempt, are ^f, becaufe there are fifty-two cards 
that may be drawn, and only twelve pictured cards 
to furnifh the defired refult. If it is wifhed to 
balance the chances on each fide, the twelve favour- 

with great clearnefs the view, common to him and to the 
writers I have named, that " the fubjeft-matter of calculations 
in the theory of probabilities is quantity of belief. In every 
problem a certain number of hypothefes are prefented to the 
mind, along with a certain quantity of information relating' 
to them : the queftion is — in what way ought belief to be dis- 
tributed among them ? " His refearches did not come under 
my notice till the text was written. 



LAWS OF THOUGHT. 333 

able muft be fubtra£ted from the whole fifty-two, 
and forty unfavourable are found to remain. Ap- 
plying this principle, we fhould fee without much 
confideration that a propofition abfolutely certain 
muft be reprefented by a unit, becaufe there is no 
difference between the number of favourable events 
and the whole events. That the card drawn will 
be of fome fuit or other is certain ; then its chance 
is \\ = 1. It is equally clear that the fymbol of a 
wholly uncertain judgment is 4, for the two chances 
are that it may come to pafs or not, and the former 
of them is the one favourable chance. Thus that a 

red card will be drawn, and not a black will be 
26 1 

ys — 2. 

To take a familiar, yet fomewhat more difficult 
problem — what are the chances, in toiling up a half- 
penny, that it will give a head at or before the third 
throw ? We afllime that the fides of the coin evenly 
balance each other, which by the way is not the 
cafe. Now here are eight events, any one of which 
may occur in three throws — 

1. No head may be thrown. 

2. The 1 ft throw only may be a head. 

3. The 2nd > 

4. The 3rd — — 

5. The 1 ft and 2nd 

6. The ift and 3rd — ■ — 



334 OUTLINE OF THE 

7. The 2nd and 3rd 

8. All three may be heads. 

Out of the eight, the firft alone is adverfe ; in all 
the reft a head is thrown at or before the third trial ; 
and according to the axiom, the favourable chances 
are feven (events,) to one (event) ; or T of the cafes 
make for us. 

That this refult is fairly calculated may be ga- 
thered from another mode of proof. Suppofe that 
eight diftinft trials are made, to fee at what throw 
the firft head comes ; we may calculate that in feven 
out of the eight trials it is likely to occur at or be- 
fore the third. As heads are as likely to be thrown 
as tails, we expeft that in half, that is four, cafes, 
heads will make their appearance the firft time. 
The fame principle applies to the other four cafes, 
in which we muft go on to a fecond throw ; in half 
of the fecond throws, that is, two, we expeft heads. 
There remain only two cafes in which it will be ne- 
cefTary to proceed to a third trial, to get the head ; 
and half of them, or one, will be heads. Thus — 

In 4 cafes, a head firft throw. 

In 2 , fecond 

In 1 , third — — . 

7 
leaving only one of the eight trials in which it will 



LAWS OF THOUGHT. 335 

be neceflary to go further. Here again we have 
feven favourable events to one unfavourable \ in 
common language the odds are kv^n to one. 

There is no difficulty in ftating the refult thus 
attained, in a fyllogifm. 

■J of the groups of three throws give a head, 
This trial is to be a group of three throws $ 
Therefore this trial (-§) will give a head. 

The fraction written after the fubje£t of the con- 
clufion is to be read M It is 7 chances out of 8 ; " 
or, taking the numerator for the chances on the 
one fide, and the difference between it and the de- 
nominator for thofe on the other, " The chances 
are 7 to 1." 

The origin of the axiom is involved in the fame 
difficulty as attends the axioms of geometry. How 
do we come to expeft that in the long run head and 
tail will nearly divide the throws between them ? 
Why do we not look for a long unbroken feries of 
one or the other ? Experience, no doubt, firft fug- 
gefted this abfolute indifference of nature to two 
events, neither of them having any known caufe that 
mould give it a preponderance. But it may ftill be 
queftioned whether the intricate calculations founded 
on this axiom are mere generalizations of experience, 
and whether our faith in the neceflary truth of the 
axiom be not more than the fum of our experiments. 



336 OUTLINE OF THE 

Certain it is that experience confirms it. In expe- 
riments made by Buffbn, by Proffeffbr de Morgan, 
and M. Quetelet, the refults coincided very clofely 
with the a priori calculation. But to verify the 
doftrine of chances by experiment, a wide range of 
fa£ts is required, becaufe a feries of a few cafes 
often exhibits great aberrations from a rule that 
never fails to vindicate itfelf in a longer courfe on 
trials. An Infurance Office with five or ten clients 
only might be ruined in a year by two deaths. In 
fome of the experiments alluded to above, a head 
was not thrown till the ioth, the 14th and the 1 6th 
throws. It is not unufual to find a family with fix 
or eight fons and no daughters ; and yet the whole 
number of male, is very nearly equal to that of 
female births throughout the world. 

2. Where the probability is a compound one, 
that is, where one uncertain event depends upon 
another, the rule is that the whole probability is af- 
certained by multiplying the chances of the feparate 
events together. Imagine a gold, a filver and a leaden 
urn, the firft containing four white and two black 
balls, the fecond and third fix white balls each ; and 
fuppofe that a man is to draw one ball blindfold 
from one of the three urns, he knows not which, 
— what are the chances of his fixing on a black 
ball ? The black ball can only be drawn from the 



LAWS OF THOUGHT. 337 

golden urn ; and the chance that he goes there at 
all is J. : if he finds that urn, the black balls in 
it are -| of the whole ; then the chances of his 
drawing a black ball are \ X \ zz T \ =z |. By 
way of proof that the fum total of the chances is not 
altered by their having been diftributed over two 
events, it is to be noticed that if all the 18 balls 
were in one urn, the chances would be exactly the 
fame. The fyllogifm would be — 

My drawing from the golden urn is \ of the 
poflible cafes, 

My drawing a black ball is § of the poflible 
drawings from that urn ; 

Therefore my drawing a black ball is ~ of the 
poflible cafes. Or — 

B is « A, 
Cis |B; 
.\ Cis £ A. 
In other words, there are 16 to 2, or 8 to 1, againft 
my drawing a black ball. 

3. To find the chance of the recurrence of an 
event already obferved, divide the number of times 
the event has been obferved, increafed by one, by the 
fame number increafed by two. If an inlander coming 
to the fea, obferved the phenomenon of the tide 
ten times in fucceflion, the chance to him that at 
the next period the tide would again rife would be 



338 OUTLINE OF THE 

10 + 2 ~ 1^ > or ii to I. Every certainty is re- 
prefented by a unit, as has been fliown ; and fo 
many units are added to the poflible cafes (deno- 
minator of the fraction) as there have been events, 
and fo many to the favourable cafes (numerator) as 
there have been favourable events. " Or, if we 
reprefent," fays M. Quetelet, " the number of times 
that the event has occurred by a fimilar number of 
white balls that we throw into an urn, adding alfo 
one other white ball and one black ball, the pro- 
bability of the reproduction will be equal to that of 
drawing a white ball." 

4. In order to calculate the probability that an 
event already obferved will be repeated any given 
number of times, the rule is, to divide the number of 
times the event has been obferved^ increafed by one^ 
by the fame number increafed by one and by the number 
of times the event is to recur. Thus, if the tide had 
been obferved 9 times, the chance that it would recur 
ten times more would be JL , ln J i = (±^-) = i 

9+10+1 \2 J 2 

" This is the fame thing as if each reproduction of 
the obferved event correfponded to putting a white 
ball in an urn where there were already, before com- 
mencing the trials, a white ball and as many black 
balls as it is fuppofed that the event obferved fhould 
re-occur times." 

5, The probability that there exifts a caufe of the 



LAWS OF THOUGHT. 339 

reproduction of any event obferved feveral times 
in fucceflion is expreiTed by a fraclion which has for 
its denominator the number 2 multiplied by itfelf as 
many times as the event has been obferved, and for its 
numerator the fame producl minus one. This has 
been called Bayes 5 rule, and its validity is not fo ge- 
nerally admitted as that of the preceding ones. 
Thus, fuppofing that two tides only had been ob- 
ferved, the chance of a caufe would be 

2x2x2 8' 

Where the obfervations have not all been fa- 
vourable, in order to eftimate whether the event 
will occur once more, the rule is to divide the 
number of times the event has been obferved to hap- 
pen increafed by one, by the total number of obfervations 
increafed bv two. Thus, if out of 26 metals known 
to the chemift, 24 are heavier than water and 2 
lighter, the chance that the next difcovered, affuming 
as certain the fa£t of difcovery, will be lighter than 
water, will be ^ % -§- = ~ 3 or 25 to 3. 

Other examples of thefe formulae may readily be 
found, to make the ufe of them eafy, and to verify 
their truth. In applying the doctrine of chances to 
that fubject in connexion with which it was invented, 
— games of chance — the principles of what has been 
happily termed " moral arithmetic " muft not be 
forgotten. Not only would it be difficult for a 



340 OUTLINE OF THE 

gamefter to find an antagonifl: on terms, as to for- 
tune and needs, precifely equal, but alfo it is impof- 
fible that with fuch an equality the advantage of a 
confiderable gain ftiould balance the harm of a ferious 
lofs. " If two men," fays Buffbn, " were to deter- 
mine to play for their whole property, what would 
be the effeft of this agreement ? The one would 
only double his fortune, and the other reduce his to 
naught. What proportion is there between the 
lofs and the gain ? The fame that there is between 
all and nothing. The gain of the one is but a mode^ 
rate fum, — the lofs of the other is numerically in- 
finite, and morally fo great that the labour of his 
whole life may not perhaps fuffice to reftore his 
property." 

The theory of chances aflifts materially in giving 
a clear conception of modality (p. 314). A propo- 
fition may pafs from abfolute uncertainty, where 
there is as much againft as for its truth (= 4) U P to 
abfolute certainty ( = 1 ) through an infinite number 
of deepening (hades of probability (|, £, T 9 ^, and fo 
on). Thefe refinements in eftimating evidence are 
little ufed in ordinary thinking, it is true ; and 
broader lines of diftin£Hon fufEce. But they feem 
to juftify thofe who exclude modality from the form 
of judgments, fince otherwife one judgment would 
feem to be capable of being modified into a hundred, 



LAWS OF THOUGHT. 341 

the expreffion remaining the fame, and the evidence 
only varying. 

Hume in his u Effay of Miracles" has overlooked 
one property of highly probable judgments — that the 
favourable evidence for them not only preponderates 
over, but utterly expels, the unfavourable, and efpe- 
cially in matters where the moral nature is con- 
cerned. The probable evidence that the fun will 
rife daily for the next ten years is exceedingly ftrong ; 
and confequently, from " the days of Noah" to the 
prefent, people have afted as if the weaker probability 
had no exiftence. If a jury find a man guilty, be- 
caufe ten credible witnefles have fworn againft him, 
and one or two for him, they confider that the tefti- 
mony of the ten annihilates that of the two ; were it 
otherwife, they muft give the prifoner the benefit of 
their doubt. A fon does not eftimate the balance in 
favour of the truth of a father's ftatement, nor a 
friend of a friend's : becaufe to doubt at all is not to 
believe. When he afferts that in the cafe of mira- 
cles, w there is a mutual deftru£tion of arguments 
[for and againft them], and the fuperior only gives us 
an aflurance fuitable to that degree of force which 
remains after deducting the inferior," he negle£h the 
diftin£tion between mathematical and moral fubje£ts; 
in the one, both favourable and adverfe chances muft 
be preferved ; in the other, that is, where we have to 



342 OUTLINE OF THE 

aft on probabilities, adverfe arguments muft, when 
once we have made up our minds, be ignored en- 
tirely, becaufe to permit them the fmalleft influence 
would weaken and fetter our a£tions. The reft of 
his argument has been fully refuted. Writers on 
probabilities have fhown how rapidly the fcale of 
belief afcends with the addition of each new inde- 
pendent witnefs ; and Paley has expofed the fallacy 
of reafoning from what is contrary to one's own ex- 
perience to what contradifts the univerfal experience 
of men. 

The numerical mode of ftatement illuftrates the 
operation of the will in moral actions. The a£tion 
entirely indeterminate, in which there is an exa£t 
equilibrium between the motives for and thofe againft 
a particular courfe, is reprefented by (fay) ~ T = \ : 
though fome maintain that except in the cafe of the 
afs of Buridanus, whofe u two bundles of hay" are no 
longer worthy of the dignity of philofophy, fo nice a 
balance cannot occur. The neceffary adtion, where 
all the motives are on one fide, is reprefented by 
\^\ = i. Between thefe extremes a vaft number of 
degrees muft exift ; and though human juftice draws 
a broad line where criminal refponfibility begins, its 
decifions muft needs be rough and inaccurate. 

The application of the do£trine of chances to real 
cafes muft be made with great caution. Our illuf- 



LAWS OF THOUGHT. 343 

trations have been drawn for the mod part from 
artificial cafes, where caufes have been ftudioufly ex- 
cluded that might have difturbed and complicated the 
refults : in nature thefe are hard to find. 



§125. Syllogifms of ClaJJification. 

Clafiification, which enters into all fciences, is the 
bafis of fome of them, as Botany, Mineralogy, and 
Zoology. In every act of clafiification two fteps 
muft be taken ; certain marks are to be felected, the 
poffeflion of which is to be the title to admiffion into 
the clafs, and then all the objects that poffefs them 
are to be afcertained. Where the marks felected 
are really important, and connected clofely with the 
nature and functions of the thing, the clarification is 
faid to be natural ; where they are fuch as do not 
affect the nature of the objects materially, and be- 
long in common to things the moft different in their 
main properties, it is artificial. 

A clafs cannot always be defined in words, fo as 
to defcribe every ipecies in it. From the loweft of 
its fubdivifions to the higheft, we pafs through fb 
many fhades of difference, that we have a difficulty 
in perceiving and expreffing the likenefs between the 
extremes ; and properties which were prominent at 
the bottom of the fcale, are in the higher fteps for- 



344 OUTLINE OF THE 

gotten, as nobler ones come into view. To diftin- 
guifh the polyp, the loweft fpecies in the animal 
feries, from a plant, it muft be defined as " having 
a digeftive cavity;" whereas the definition ufually 
given for higher animals, and for the conception ani- 
mal in general, conveys that they are " beings en- 
dowed with life and fenfation." Still we group 
them together by our perception of likenefs ; which 
though not fo obvioufly applicable to the ends of the 
feries viewed together, and apart from the interme- 
diate links, becomes fo when we pafs regularly along 
the chain. We might not be able to prove that the 
polyp had fenfation at all, if there were not creatures 
a little higher in the fcale of being, refembling the 
polyp in other particulars, and exhibiting more 
plainly the knk of feeling. We prefume that it 
exifts in the lower, becaufe we fee it in the higher, 
and though it decreafes as we defcend, we cannot 
fhow that it has ceafed. The definition of a genus 
is the adequate definition of its loweft fpecies only, 
fince one which included any higher properties than 
the loweft exhibits, would of courfe exclude it. But 
in claffification, the definition is not fo much ufed as 
the type, that is, fome one pattern fpecies, by likenefs 
or unlikenefs to which we arrange the others, and 
affign them a higher or lower degree. 

Though the fpecies in any great clafs rife by the 



LAWS OF THOUGHT. 345 

fteps of a regular arrangement, the fame feries muft 
not be continued from the highefl: of one kingdom to 
the loweft of the next above it. The highefl: plant 
is often confidered next below the loweft animal, 
whereas it is much more like, though infinitely in- 
ferior to, the highefl: animal. The animal, vegetable 
and mineral kingdoms rather refemble ladders of 
equal height refting upon three different fteps of a 
houfe, than ladders raifed one upon the other. The 
loweft animal, the loweft plant, and the loweft mi- 
neral anfwer to each other ; and the complex animal 
organifm, the tall and beautiful tree, and the regular 
group of cryftals correfpond in fome meafure at the 
top of the refpe£tive fcales. 

A fyllogifm like the following is adapted to exprefs 

claffification. 

U A A, Fig. 1. 
All beings endowed with life and fenfation = animals, 
The polyp .... the man have life and fenfation; 
Therefore they are animals. 

§ 126. Nomenclature. 

The fourth queftion to be anfwered was — how 
fhall new laws be exprefTed and recorded ? It has 
been ftiown already (p. 42), that names are ufeful in 
preferving the refults of new difcoveries and reafon- 
ings, and that without fuch means fcience could 
never fecure its gains, nor reproduce them with the 



346 OUTLINE OF THE 

neceflary celerity. Let any one confider how much 
is meant by chemical affinity^ atomic weighty capital^ 
inverfe proportion^ polarity ^ means and limits ; how 
theories are here gathered up into a fingle word, and 
pafled readily from mind to mind ; and he will admit 
the parallel between words and that paper money by 
which the ponderous wealth of the world may be 
enclofed in envelopes, and pafled fwiftly from hence 
to the antipodes. Hence every progreffive fcience 
muft conftantly enlarge its ftore of names and words. 
Four ways are open to it of doing fo. * 

i. Names already in ufe may be adapted to new 
meanings, by frefh definitions. Thus fait has been 
extended, from the condiment ftill known by that 
name, to a great clafs of compound bodies known to 
the chemift. Force^ attraclion^ affinity afford oth^r 
examples. 

2. Names that contain their own explanation 
may be formed, to reprefent new ideas ; as ifomorphifm^ 
for the identity of the cryftalline forms of fome che- 
mical bodies ; Trgoalgso-ig, to exprefs the previous 
choice or purpofe which makes our actions morally 
imputable to us ; homoeopathy for the fyftem of me- 
dicine that profefles to cure by medicines that pro- 

* For fuller illuftrations fee WhewelVs Philofophy of the 
Inductive Sciences. 



LAWS OF THOUGHT. 347 

duce effects like the difeafe. Names fo conftrudted 
will often embody a theory, and mould be difcarded 
if it turns out to be untrue. 

3. The invention of a wholly new name, un- 
meaning in itfelf, but accompanied by a precife defi- 
nition, is free from fome of the dangers that befet the 
other modes ; for old words are often ufed vaguely, 
becaufe they have obtained a footing before their 
fcientific meaning has been given them, and new 
names that convey their own explanation are often 
cumbrous, and in fome cafes do not permit the 
erroneous theory they carry on their face, to be 
amended. An attempt of this kind has been made 
by Von Reichenbach, in defignating a new force he 
believes that he has difcovered, by the name Od- 
force. Such a name, whatever be thought of the 
theory it belongs to, feems well devifed ; it is fhort 
and eafy of ufe, and it enters readily into compounds, 
as Odyle, Thermodyle, and fo on. 

4. Chemiftry affords good examples of the mode 
of forming new names by fyftematic alterations of 
old well-known ones. Thus from fulphur we have 
fulphide^fulphite^fulphate^ bifulphate^ &c, and each 
of thefe is appropriated to a particular chemical con- 
ftitution. Such a plan feems to obviate the objec- 
tions on the fcore of novelty, vaguenefs and tranfi- 
torinefs, to which other methods are open. 



348 OUTLINE OF THE 

§ 127. Sources of Principles. 

The inductive and dedu&ive procefles prefuppofe 
fome principles from which they may commence. 
A principle might be defined as that from which 
reafoning begins. 

Obfervation, either by means of the fenfes unaided, 
or by the affiftance of inftruments, furnifhes the 
principles of induftive reafoning. Where ifolated 
obfervations are of lefs value, from their fluctuations, 
as in eftimating the temperature of a country, the 
weight of the atmofphere, and the like, the doc- 
trine of means is applied to an extended feries of 
obfervations. By it, the fum of the refults of the 
obfervations is divided by the number of obferva- 
tions taken, and the quotient is the mean. Although 
this may happen not to correfpond exactly with a 
fingle obfervation, yet in a large number of them it 
is found that the majority range themfelves clofely 
round the mean, and that the number diminifhes with 
furprifing regularity as we approach either extreme. 
Thus, if the mean temperature on a given day in the 
year be 6o° Fahrenheit, as afcertained from the ob- 
fervation of a hundred years, and 50 and 70 be the 
extremes on either fide, we mall find on arranging 
the fingle obfervations that moft of them duller as 
it were around 6o c , whilft one or two only coincide 



LAWS OF THOUGHT. 349 

with each extreme ; and that as the mean is ap- 
proached, fay by intervals of two degrees, the number 
of coincident obfervations grows greater at each ftep 
till the mean is reached. A full explanation, intel- 
ligible to all, of this moft interefting fubjeft, is given 
in Quetelet's work " On Probabilities." Where a 
mean is taken, without any need for arranging the 
feveral obfervations according to their approach to it, 
it has been called an average ; the refults of the har- 
veft, and the prices of corn, are eftimated in this way 
every year, the former roughly, the latter with arith- 
metical accuracy. 

Historical records are obfervations which reft upon 
the teftimony of others ; of thefe the moft important 
are the records of religious hiftory, which reft upon 
outward teftimony accepted and confirmed by the 
inward religious confcioufnefs. 

Deductive principles are certain univerfal propor- 
tions gained in various ways. Theological principles 
are the truths of the divine law, made known to man 
by infpiration ; univerfal, but not generalized from 
experience by obfervation. Natural principles are 
propofitions in morals, government, and the like, 
upon which there is a general agreement founded 
upon a natural inftindh Mathematical principles are 
propofitions about fpace and number, to which the 
reafon cannot but aflfent, without requiring to verify 



350 



OUTLINE OF THE 



them by new trials ; fuch are the definitions and 
axioms of geometry. Pofitive principles have been 
gained by reafoning upon former experience ; they 
are either the definitions of the mixed fciences, or 
divifions of their fubjeft matter, or hypothefes laid 
down to be verified by future comparifon with fafts. 



TABLE OF PRINCIPLES. 

N.B. This is not a perfect logical divifion ; ex. gr. " Ob- 
fervations" may depend on teftimony and {o be " hiftorical." 

(Without inftruments 
With inftruments 






Principles - 



Inductive 



Aggregate 
Obiervations 



" Scale of means and 
limits 



Deductive -< 



Simple averages. 
Hiftorical Records. 
" Theological 

Mathematical 

Natural 

' Definitions 

Pofitive -l Divifions 

^ Hypothefes. 



LAWS OF THOUGHT. 351 

§ 128. Errors and Fallacies. 
Not one logical principle can be put in practice 
without the poffibility of error. Where an error is 
latent, and tends to deceive either the thinker or 
thofe to whom he offers it, the name of fallacy is 
given to it. A complete lift of fallacies would in- 
clude one or more for every one of the procefTes of 
thinking; and, after all, the expofure of material errors 
can only be effected with advantage by each feparate 
fcience for its own department, as has been done for 
Political Economy in the " Sophifmes Economiques" 
of M. Baftiat. Formal errors are only deviations from 
the laws of thought already laid down, as, for ex- 
ample, by making an incomplete divifion, or by 
holding contradictory judgments together, or by 
drawing a conclufion too broad for the premifes. 

§ 129. Dealing with Errors. 

When oppofing arguments are to be dealt with, 
we may either aflail one of the premifes by an In- 
Jlance (EvcrraaLg) to the contrary of what it aflerts; or 
we may dij/olve (xueiv) the argument by ftiowing its 
unfitnefs for proof becaufe of fome formal defeat, as 
where a univerfal is proved from a few particulars. 
Or, admitting the apparent corre£tnefs of the oppof- 
ing argument, we may prove the contradictory of its 



352 OUTLINE OF THE 

conclufion by an unavailable argument of our own, 
which is thencalled an Elenchus (sxeyxog). Or laftly, 
we may fortify our own argument by " a reduction 
to impoffibility," that is, by ftiowing that fomething 
impoffible or abfurd follows from contradiding our 
conclufion ; this is called indirect demonft ration, as 
it goes round to prove that a thing is by fhowing 
what abfurdity would follow if it was not, and thus 
differs from the dire£t mode, which proves dire£Uy 
from premiffes that the thing is.* 

B. Arrangement of a Science. 

§130. Method. Definition and Divifton. 

As method in the higheft fenfe is a natural gift 
rather than a technical fyftem, it can be belt under- 
stood by ftudying a few examples, which have pro- 
ceeded from minds of the higheft order. It will be 
found that whilft the deductive and the inductive 
orders have been followed, with the aid of definition 
and divifion, none of thefe means has been exclu- 
sively employed ; and the due admixture of them, 
and the degree of preponderance to be afligned to 



* Inftance, Pri. An. it. 26 5 Solution of an argument, Rhet. 
I. 2, Pri. An. II. 27 ; Elenchus, Pri. An. II. 20 5 Reduction 
to Impoffibility, Pri. An. I. 23, Poll. An. I. 26. 



LAWS OF THOUGHT. 353 

any one, have been regulated by the imagination and 
tafte of the conftru£tor. In " Euclid's Elements/' 
the nature of the fubje£t, which is independent of 
verification from facts, permits an almoft exclufively 
dedu&ive order to prevail, which proceeds from de- 
finitions and axioms, and difpenfes with divifion. In 
" Plato's Republic," one of the nobleft examples of 
method, fucceffive definitions of juftice are brought 
to the teft and rejected ; and then divifion prepon- 
derates, in the enumeration of the powers of the 
human foul, and of the clafles in a ftate that anfwer 
to them ; as well as of the declinations through which 
the perfe£t polity, if it could be conftru£ted, would 
have to pafs. The whole is fufed together and 
adorned by a dramatic element, in fuch a manner as 
to render this dialogue the fineft work of pagan phi- 
lofophy. In the " Nicomachean Ethics" of Arif- 
totle definition predominates, but with confiderable 
aid from divifion. Thus he enumerates the opinions 
of men about " the good," and reje&s all but the 
right one ; defining that, under the name of " hap- 
pinefs," he is led on to define the parts of his firfr. 
definition ; and in the cafe of the moral and intel- 
lectual virtues he does not confider his explanation 
complete without an enumeration (or divifion) of 
both clafles. In fubordinate portions, good examples 
of divifion are alfo found ; and in the concluding 

A A 



354 OUTLINE OF THE 

chapters of Book VI., and in other places, difcuflions 
upon nominal definitions, or the fenfes which various 
Greek nouns bear, are alfo introduced. The text 
books of chemiftry, mineralogy, botany, and zoology, 
will afford good examples of divifion, bafed upon de- 
finition ; a clafs or type is defined, and the fpecies 
enumerated and examined. 

The clofe relationfhip between definition and di- 
vifion will be evident to the ftudent who examines 
fuch examples carefully. In truth, wherever a divi- 
fion is made upon fome natural, and not merely ac- 
cidental ground, every ftep of it furnifhes fome dif- 
tinitive mark, which- will naturally make its appear- 
ance in a definition afterwards. Again, as every 
definition, properly fo called, fets forth diftin&ive 
marks of the conception defined, it gives at the fame 
time the means of dividing or feparating it from 
other clafTes. In order to fecure this mutual co- 
operation, Ariftotle lays down, that in dividing in 
order to define, a real genus fhould be taken, to 
which the differences fhould be added in regular or- 
der ; that every dividing fpecies fhould be enumerated ; 
and that each new difference fhould be founded upon, 
and divide, the foregoing one (foapopm haQogav) — 
thus, it would be better, after dividing bodies into 
living and not living (p, 104), to fubdivide living 
bodies into thofe which have fentient life, and thofe 



LAWS OF THOUGHT. 355 

without it, rather than into terreftrial and aquatic, 
which would have nothing to do with the former 
difference.* 

§ 131. Subordinate parts of a Science. 

Judgments that relate to fpeculation only, are called 
theoretical ; thofe which refer to practice are prac- 
tical. Judgments that require or admit of proof, are 
called demonftrable ; thofe which are manifeft from 
the very terms, are indemonftrable. Thus much be- 
ing premifed we can define certain fubordinate parts 
of a fcience. 

An Axiom is an indemonftrable theoretical judg- 
ment. A Poftulate is an indemonftrable pra&ical 
judgment. A Theorem is a demonftrable theore- 
tical judgment. A Problem is a demonftrable prac- 
tical judgment. A Thefis is a judgment propofed 
for difcuffion and proof; (but with Ariftotle itfome- 
times means an axiom of fome fpecial fcience or dif- 
putation). A Hypothefis is a judgment provifionally 
accepted as an explanation of fome group of facts, 
and is liable to be difcarded if it is found inconfiftent 
with them. A judgment which follows immediately 
from another, is fometimes called a Corollarv or Con- 
feftary. One which does not properly belong to the 

* See An. Poll. II. xiii. 7 (97, a.) Met. VII. 12 (1038. a.). 



356 OUTLINE OF THE 

fcience in which it appears, but is taken from an- 
other, is called a Lemma. One which illuftrates the 
fcience where it appears, but is not an integral part of 
it, is a Scholion. 



§ 132. Categories. 

Whilft pure Logic negle&s the real nature of the 
things it deals with, and attaches to them only a for- 
mal value, logicians in almoft every age have endea- 
voured to form fchemes of claflification in which 
things fhould be arranged according to their real 
nature. Logic deals, as we have feen, with fecond 
intentions, but it has been found defirable to make 
clafles for firft intentions alfo. To thefe clafles the 
name of Categories, or as we might render it Attri- 
butions, has been given ; for whilft they are clafles 
of things and not of propofitions, fo that they do not 
properly attribute any quality to a fubje£t, they are 
conftrufted with a view to the more ready difcovery 
of attributes when required. They are intended, 
like the labelled drawers in a cabinet, to be a well 
arranged repofitory of the treafures of thought and 
knowledge, in which they may be kept fecure and 
ready for ufe. Such a fyftem of arrangement for 
things and the attributes of things is eflentially meta- 
phyfical, and if admitted into Logic at all, muft belong 



LAWS OF THOUGHT. 357 

to the application of it, wherein we employ the pure 
forms of thought to difcover the nature of things. 

We require of a good fyftem of Categories that it 
provide a place for every fimple notion, and that its 
heads or divifions be fpecific enough to furnifh real 
help in finding the attributes of any fubjeft ; in two 
words, that it be exhauftive and fuggeftive. Tried 
by this teft, fuch divifions as that into Subftance, 
Mode, and Relation will be rejected as comparative! v 
ufelefs ; if complete and exhauftive, they are too 
vague to offer any tangible fuggeftions. Even the 
more elaborate divifion of Ariftotle is open to this 
charge ; not to dwell upon the accufations fometimes 
made, that it is confufed and incomplete. He divides 
words or notions into ten claffes, viz. Subftance, 
Quantity, Quality, Relation, Place, Time, Pofition, 
Mode of Being, Doing, and Suffering. Trendelen- 
burg finds an exa£t correfpondence between thefe 
and the grammatical divifion of the parts of fpeech ; 
the firft four correfponding to Subftantives and Ad- 
jectives, the next two to Adverbs, and the laft four 
to the aftive, paffive and neuter Verbs ; but perhaps 
he pufties a good fuggeftion, that Ariftotle fought in 
language the ground work of his arrangement, fome- 
what too far. Another important fuggeftion would 
reduce the number of the principal Categories to 
four, Subftance, Quantity, Quality, and Relation ; 



358 



OUTLINE OF THE 



of the laft of which the remaining fix are only fub- 
divifions, for Place and Time are the relation of 
things to each other in fpace and time, and the re- 
maining four imply connexion with other things.* 
Another divifion of Categories may be juft at- 
tempted. 

TABLE OF THE CATEGORIES. 
P 

Substance 



bC 



o 
U 



Quantity 



Attribute -j Quality 



Relation 



r of Time 

ofSPACE 
ofCAUSATION 

of Composition 

of Agreement &Repug- 

NANCE 

of Polar Opposition 
.of Finite to Infinite. 



The ultimate members in this divifion are ten in 
number — an accidental coincidence with the Arifto- 



* See Stallbaum, Parmenides, Prol. p. 170. For the hif- 
tory of Categories fee ProfefTor Trendelenburg's Gefchichte 
der Kategorienlehre, and for the Hindu Syftem of Kanada, 
fee the Appendix to the prefent work. 



LAWS OF THOUGHT. 359 

telian lift. They are— Subftance, Quantity, Qua- 
lity, Relation of Time, of Space, of Caufation, of 
Compofition, of Agreement, of Polar Oppofition, 
and of Finite things to the Infinite. Moft of thefe 
names will be underftood by every perfon likely to 
ftudy a fyftem of Categories ; and as it is necefTary 
at prefent to ftate refults only, they may be paffed 
over without comment. The ninth in the lift how- 
ever, the Relation of Polar Oppofition, may not fo 
eafily be underftood. We find that in different parts 
of the field of knowledge pairs of oppofite things 
unite and form a new whole different from either of 
them. In Morals, Ariftotle's doctrine of the Mean 
is a cafe in point : courage, for example, is regarded 
as the line of indifference between audacity and an 
undue fenfe of danger, and the notion of it is not 
complete without both thefe elements. In Chemiftry, 
the neutral falts, and the ftate of equilibrium of pofi- 
tive and negative electricity, are examples. In Art, 
the neceffity of a balance of confcious activity and 
the unconfcious natural energy, of the critical and 
creative faculties, may, if Schelling be correct:, fup- 
ply another. A large number of paffages from va- 
rious authors have been collected, which fhow how 
different minds occupied on different fubjects, not 
excluding the higheft of all, religion, fall into this 
law without knowing it. And when we fpeak of 



360 OUTLINE OF THE 

"half-truths" or reprehend men for their "one- 
fidednefs," in reality our ground of complaint is that 
this law has been broken or overlooked. Rafhnefs 
is often confidered courage ; and diligent ftudy of art 
pafles for artiftic (kill. The neceffitarian, the hafty 
theorift, the fuperftitious, are victims of half-appre- 
hended truths, which turn into deadly errors ; and 
it would not be hard to ftiow that the whole tafk of 
a great thinker has often been to call attention to the 
oppofite element, too much overlooked, and to unite 
what common minds have decompofed. 

Alterius fie 
Altera pofcit opem res, et conjurat amice. 

But this fubjeft is worthy of a fuller illuftration 
than can be afforded it here. 



§ 133. A Divijion of the Sciences. 

T he table of Categories enables us to afcertain 
what kinds of attributes may belong to any con- 
ception, no matter from what department of know- 
ledge it may be taken ; confequently it is applicable 
to all fciences. A divifion of the fciences, on the 
other hand, tends to feparate different diftri&s of 
knowledge, with the conceptions that belong to them, 
from one another. It is defirable to attempt fuch a 



LAWS OF THOUGHT. 



361 



divifion, as the conclufion of a treatife on Logic ; if 
for no other reafon, in order that we may know to 
how many fubje£ts we may have to dire£t our rules. 
A fcience is a fyftematic arrangement of all the 
laws which belong to any one fubjeft. The three 
great fields of human refearch are — the Divine Na- 
ture, the nature of the human mind, and the nature 
of the univerfe ; and correfponding to them are three 
principal groups of fciences — the Theological, the 
Pfychological, and the Cofmical or Natural. Of the 
members of each group different enumerations may 
be given. In the prefent attempt, large affiftance 
has been derived from the work of M. A. M. Ampere 
on the Claffification of the Sciences, from Dr. 
Whewell's Works, Weife's Archite£tonik, and other 
fources, but efpecially from the work firft named. 
An eloquent and philofophic writer, Mr. George 
Ramfay, has alfo publifhed a tra£t upon the claffifica- 
tion of the fciences. 



THEOLOGICAL SCIENCES. 



Theology. < 



Biblical 



Syftematical 



Hiftorical 



Biblical Criticiim. 
Expofition — Exegefis. 
Dogmatic Theology. 
Paftoral Theology. 
Church Hiftory. 
Hiftory of Doctrines. 



362 



OUTLINE OF THE 



MENTAL SCIENCES. 



Mental 

Sciences. 



Reafon 



Choice and 
Aife&ion 



Logic, or the Science of the 
forms of Thought. 

Metaphyfie, which examines 
the ground of all know- 
ledge of things, 
r Morality, founded on the 
Conception of Right. 

JEfthetic, founded on the 
Conception of Beauty. 



Mathema- 
tical 
Sciences. 



Physical 
Sciences. 



Natural 
Sciences. 



Medical 
Sciences. 



COSMICAL SCIENCES. 

r Pure Mathe- ( Arithmetic. 

matics (. 

I Phyfico-Ma- 
L thematics 



Geometry. 
( Mechanics. 
( Aftronomy. 

r General Phyfics. 
j Technology, or Phyfics ap- 
plied to Arts and Manu- 

<- failures. 

f Defcriptiye Geology. 
< Mining, or " Ory&otechny." 

<- (Ampere.) 

( Botany. 

{Y ° \ Agriculture. 
r Zoology proper. 
Zoological < Zootechny, knowledge of the 
I ufe of animals to man. 



Phyfics pro- 
per 

^ Geology 



r Phyfico-Me- ( Medical Phyfics. 
J dical 1 Hygiene. 



1 Medical Sci- C Pathology. 

L ence proper ( Practical Medicine. 



LAWS OF THOUGHT. 



363 



Political 
Sciences. 



1 



Pal^etio- 

LOGICAL 

Science.* 



Leghlation -j 



! 



^ Government 



Political Economy. 

Hiftory of Laws and Con. 

ftitutions. 
Adminiftration of Law. 
Police and Defence. 

{Hiftorical Geology. 
Diftribution of Plants and 
Animals. 
fGloflblogy, or fcience of affi- 
nity of languages. 
Ethnography, or fcience or 
affinity of races. 






§ 134. Conclufion. 

Thefe hints may be fufficient to guide a ftudent in 
applying the principles of Pure Logic to the practice 
of analyfis.f 

If this little work is haftily examined and caft 
afide, of courfe the reader will not have become a 



* i. e. Sciences in which the object is to afcend from the 
prefent ftate of things to a more ancient condition, from which 
the prefent is derived by intelligible caufes. 

f They are not intended to fuperfede a reference to fuch 
works as Whewell's Inductive Sciences, Herfchel's Prelimi- 
nary Difcourfe, and Mill's Logic ; to induce the reader to carry 
his refearches on to thefe and fimilar productions is their chief 
object. Thefe writers have allotted a larger fpace forthemoft 
part to the fpecial fciences and their hiftory than was com- 
patible with the prefent attempt, even if fufficient learning and 
ability had been at command. 



364 OUTLINE OF THE 

logician ; he will have learned the unimportant fa£i 
that upon this or that difputed do£trine the author 
held this or that opinion, and his knowledge will go 
no further. Inftead of learning Logic, he will know 
an infignificant fa£t in logical hiftory. The miftake 
is not uncommon ; — we enquire what Ariftotle and 
Bifhop Butler faid on morality, and think that we 
have ftudied Moral Philofophy ; we read the Or- 
ganon, and call ourfelves logicians. Hiftory prefides 
over thefe and other fa£ts ; we are in her domain 
when we ufe our books in this narrow fpirit. Phi- 
lofophy does not exift until the mind of the ftudent 
begins to work for itfelf with the principles it re- 
ceives hiftorically; to decompofe and to compofe 
anew, to criticize the arguments employed, to eflay 
at leaft to pufli the confines of truth farther into the 
wilds of error and ignorance, and to leave her a wider 
territory. 

If Grammar is learnt by fpeaking and writing, if 
a man cannot become an orator without repeated 
efforts to fpeak in public, nor a poet without prac- 
tifing the mechanifm of verfe, till he can ufe it with 
eafe, it feems abfurd to expe£t that a courfe of lec- 
tures heard, with a ftring of definitions learnt, will 
make a logician. 

Let thofe who wifh to poffefs the intellect they 
have received from above, in the depth and clearnefs, 



LAWS OF THOUGHT. 365 

the fober compofure, the calm a&ivity which a high 
degree of culture can alone beftow, venture to ftudy 
Logic in a larger fpirit than the merely hiftorical. 
Let them become dialecticians ; not in the fenfe 
which the fophift attached to that name, but rather 
in that which the fcourge of fophifts gave it. Let 
them not ufe fo excellent a weapon as the reafon in 
mere play, with a guarded point and bated edge, but 
let them keep it fheathed, fharpened and mining, till 
a battle has to be fought againft an error. Let them 
watch for themfelves the procefles gone through in 
completing any fcience. If the rules given in books 
are erroneous, let them try to correcSt; if imperfe6t, 
to complete them : or, if experience verifies their 
truth and utility, let them be regarded with a degree 
of truft greater than could have been awarded to 
them before, when they flood in books, the mere 
hiftorical record of other men's philofophy. No one 
who has ftudied Logic in this confcientious fpirit has 
ever found it trifling or ufelefs. 



APPENDIX. 



ON INDIAN LOGIC. 





ON INDIAN LOGIC* 

' HE fciences of Logic and of Grammar were, as 
far as hiftory allows us to judge, invented or 
originally conceived by two nations only, by 
Hindus and Greeks. All other nations, if they 
ever cultivated thefe fciences, received the firft impulfe from 
without. The Romans from the Greeks, the Germans from 
the Romans, the Arabs from the Greeks, the Jews from the 
Arabs. 

That the two moft highly gifted nations of the world, the 
Hindus and the Greeks, mould both have been led, each in its 
own way, to a ftady of the laws of thought and the laws of 
language, feems in itfelf perfectly natural. But there is a 
certain weaknefs in the human mind, which is not fatisfied 
unlefs it fucceeds in comprehending everything under a fyf- 
tem, and reducing all multiplicity to a unity. Particularly 
when a great variety has once been brought back to a dual- 
iftic arrangement, is it confidered almoft irrational to ftop 
before the two ftreams are finally traced back to one com- 
mon fource. The fame happened here. Numerous works on 
Logic exifted, written in various languages, oriental and occi- 
dental. But it was not difficult to mow that their authors had 
all, mediately or immediately, received the flrft elements of this 
fcience from the Greeks. The Greeks were therefore confi- 
dered as the fole inventors of Logic. 

* Communicated by ProfefTor Max Miilier. 
B B 



370 APPENDIX. 

When, however, the different fyftems of Hindu philofophy 
became known to the fcholars of Europe, at the beginning of 
this century, it was found that in India alfo the fcience of 
Logic had been cultivated with confiderable fuccefs. 

Every thing that came from the Eaft was at that time looked 
upon with myfterious awe. There had been vague traditions 
of Indian wifdom long before the time of Ariftotle. There 
were reports of early Greek philofophers travelling to India 
as the fountain-head of ancient wifdom. Alexander himfelf 
had found himfelf in India face to face with a whole nation of 
philofophers. It was readily admitted, therefore, by moft 
people, that the Hindu fyilem of Logic was more ancient than 
that of Ariftotle. 

But then, how extraordinary if Ariftotle mould have hap- 
pened to found the firft fyftem of Logic in the Weft, at the 
very fame time when his pupil Alexander was converfmg with 
the Logicians of the Eaft! Much more fimple, indeed, to 
fuppofe that Alexander fent fome Indian treatifes on Logic to 
his tutor at home, and that Ariftotle worked them up into a 
fyftem of his own ! This view was actually taken by men 
like Gorres.* There were fo many points of coincidence too 
in both fyftems of Logic. In each there were Categories, Ge- 
nus, and Species, and even Syllogifm ! It could not be other- 
wife — either the Greeks muft have borrowed it from the Hin- 
dus, or 'vice <uerfd. That two nations, if they once conceived 
the idea of analyfmg the laws of thought, could pofflbly arrive 
at ftmilar refults even on the moft general points, and that it 
would require a coincidence in many minute details or in pal- 



* G*6rres even undertook to prove that the Greeks had borrowed 
fome technical names from the Sanfkrit. Indian philofophers admit 
five elements, and the fifth is called akafa, ether. This ether has quite 
a different meaning from the alOrjp which fome Greek philofophers 
confidered as the filth or higheft element. G'orres, however, quotes 
Ariftotle without giving a reference, as having mentioned this fifth 
element as ctKOT-ovofxarov, which he tranflates by ' akaf-nominatum,' 
cLKOT-ovofxarov being evidently an ingenious conjecture for aKarovo- 

JJ.UGTOV. 



ON INDIAN LOGIC. 371 

pable errors, to prove beyond doubt that the two fyftems had 
a common origin, feems never to have occurred to thefe logical 
unitarians. 

But on the other hand, does it mow a higher power of lo- 
gical reafoning or hiftorical criticifm, if we find men like Nie- 
buhr taking the oppofite view of the matter, and deriving 
Indian philofophy from Greece ? Niebuhr is reported to 
have faid in his Lectures on Ancient Hiftory, " If we look at 
Indian Philofophy, we difcern traces of a great fimilarity with 
that of the Greeks. Now as people have given up the hypo- 
thecs, that Greek philofophy formed itfelf after Indian philo- 
fophy, we cannot explain this fimilarity except by the inter- 
courfe which the Indians had with the Graeco-macedonic kings 
of Bactra." 

To Niebuhr and to moft Greek fcholars it would naturally 
be next to impoffible to believe that Greek Logic and Greek 
philofophy in general were of foreign origin and a mere 
importation from India. They know how Greek philofo- 
phy grew up gradually, how its courfe runs parallel with the 
progrefs of Grecian poetry, art, and civilization. They know 
that it is a home-grown production as certainly as that Plato 
and Ariftotle were Greeks and not Brahmans. 

But, then, a Sanfkrit fcholar has juft the fame conviction 
with regard to Indian philofophy. He can mow how the firft 
philofophical ideas, though under a vague form, exifted already 
in the mind of the early poets of the Veda. He can trace 
their gradual development in the Brdhmanas. He can fhow 
how they give rife to difcuflions, how they take a more diftinct 
form, and are at laft fixed and determined in the moft fcientific 
manner. He too is as certain that Indian philofophy was a 
native production of India, as that Gotama and Kanada were 
Hindus and not Greeks. 

Until, therefore, it can be proved hiftorically that Greeks 
received their philofophy from India or Indians from Greece 
— or until coincidences can be pointed out which it is impof- 
fible to explain otherwife, it will be bell to confider both Greek 



372 APPENDIX. 

and Indian philofophy as autochthon ie, and to derive from 
their mutual companion only this confolatory conviction, that 
in philofophy alfo there is a certain amount of truth which 
forms the common heirloom of mankind, and can be difcovered 
by all nations if they fearch for it with honefty and perfe- 
verance. 

According to the accounts which the Brahmans themfelves 
give of the hiftory of Indian philofophy, there have been, and 
there ftill exift, fix fyftems of philofophy. They are called the 
Sankhya, Mimanfa, Nyaya, Yoga, Vaifefhika and Vedanta. 
Thefe fyftems are not reprefented to us in a fucceffive order, 
they do not apparently arife one upon the ruins of the other, 
like the fchools in the hiftory of Greek and German philofo- 
phy. They always feem to run parallel, each maintaining its 
place fide by fide with the others, and each reprefenting a dif- 
tin£f. view of the Univerfe, and of the relation of the feeming 
to the real world. Even at the prefent day the Brahman 
unites three or more of them in his courfe of ftudy. 

Each of thefe fyftems is complete in itfelf. Each contains 
fomething of what we mould call Phyfics, Metaphyfics, Lo- 
gic, and even Ethics. In one fyftem, however, certain topics 
occupy a more prominent place and are difcufled at greater 
length than in another. Thus, while the Mimanfa is more 
theological, and the Sankhya more metaphyfical, the Nyaya 
fyftem, in which the reafoning faculties of man are more 
clofely examined, has become known to us by the name of 
" Indian Logic." In India alfo, a Naiyayika, or follower of 
the Nyaya, means as much as a Logician, or a man who un- 
derftands the laws of reafoning, and ftill more the art of logi- 
cal wrangling. The other fyftems refer to the Nyaya, when- 
ever logicarqueftions have to be fettled. 

Neverthelefs, it would be wrong to call the Nyaya, Logic, 
in our fenfe of the word. The Nyaya, as well as the other 
fyftems, has for its higheft object the folution of the problem 
of exiftence, and only as a means towards accomplifhing this 



ON INDIAN LOGIC. 373 

objecl, does it devote particular attention to the inftruments of 
knowledge — and, as one of them, to fyllogiftic reafoning. 

In order to explain what in the mind of a Hindu philofo- 
pher would correfpond to our Logic, it will be neceffary to 
give a fhort flcetch of the Nyaya. We mail there fee the exact 
place which Logic occupies in the fyftem of Hindu philofophy, 
and be able to judge how far it correfponds to that which 
Ariftotle and other philofophers after him have afiigned to this 
philofophical difcipline. The reafon why the Nyaya is chofen 
in preference to other fyftems, is not becaufe it alone contains 
an account of the fyllogifm. The fyllogifm finds its place in 
the Vedanta and Sankhya as well ; but it is more fully treated 
by the Naiyayikas. Again, Kanada's work, called the Vaife- 
fhika philofophy, is chofen in preference to the Nyaya-futras 
of Gotama, becaufe there is fo much of minute technicality 
in the latter, that it would become very difficult to give a 
complete account of it in a fhort compafs. 

Kanada ftarts boldly by declaring that he is going to ex- 
plain how a man can obtain the moft exalted and exalting 
knowledge of reality, and by means thereof arrive at a ftate 
of complete bleffednefs, the Summum Bonum. The way to 
bleffednefs, according to him, is knowledge, but knowledge 
of a particular kind, that is to fay, a difcriminating knowledge 
of the feven^ Categories. 

Thefe Categories are, Subftance, Quality, Action, Genus, 
Individuality, Concretion, and Non-exiftence. 



* Originally there were but fix, Non-exiftence being omitted in 
KanaoVs Sutras. Theftatements given here are taken from Annam- 
bhatta's Tarkafangraha publifhed at Benares without the name of the 
editor. This publication, and many moft valuable works lately ifTued 
from the Sanfkrit College of Benares, are due to Dr. Ballantyne, the 
Principal of this College. A Hindoftani tranflation together with an 
Englifh tranflation was alfo publifhed at Benares, from the hand 
of Mr. F. Edward Hall, though without his name. Both thefe 
fcholars have rendered great fervice to Sanfkrit philology, and have 
made the Sanfkrit College of Benares a real Exchange of Indian and 
European learning. 



374 J PP END IX. 

The Sanfkrit word which has been tranflated by category is 
'padartha,' which in common ufage means a thing. The 
etymological figniflcation, however, is ' meaning of words,' 
which, if interpreted philofophically, comes to exprefs c the 
moll general meaning of words,' ' what is common to all 
words,' what is predicated by words without any regard to 
their fpecial meaning, as given in the Dictionary. Like the 
Categories of the Greek fyftem, the Padarthas are wide claffes 
of " firft intentions." They are the laft and higheft predi- 
cates, and the only thing that can be predicated of them ac- 
cording to Vifvanatha, is their ' perceptibility.' 

But does this perceptibility involve their reality ? We muft 
hear the objections which the Hindu Materialift raifes againft 
this fuppofition. Taking the firft category, that of fubftance, 
he fays, * Ail we really perceive if we fpeak for inftance of 
water, is water. We do not perceive anything of water being 
a fubftance. Therefore you have no right to fpeak of fub- 
ftance as a category.' But, anfwers the Vaifefhika, though 
we do not perceive fubftance with our eyes, yet we perceive 
that there muft be fomething in which qualities can reiide, 
which remains unchanged though the qualities change, which 
refts the fame whether it becomes a caufe or an effect. This, 
then, we call fubftance. Quality, again, is what refides 
in a fubftance. Quality itfelf has no qualities, but fubftance 
has. Quality produces by itfelf no change. What produces 
change, or combination and feparation of qualities, is what we 
comprehend under the third Category, or Action, and this alfo 
refides in fubftance only. 

Thefe are the three principal categories, and they feem to 
correfpond very nearly with Ariftotle's ola-la, ttoUv and noe-ov, and 
ttojhTV. After thefe three, follow the two categories of Genus 
and Individuality. Genus refides in Subftance, Quality, and 
Action, and it is twofold, higher or lower. The higheft genus, 
which is fhared by everything, is ' being,' the fummum genus. 
Next to it we get as lo<wer genus that of being a categoiy, of 
being fubftance, earth, a clod, etc. Individuality is endlefs. 



ON INDIAN LOGIC. 375 

It refides in fubftance only, and as we fhall fee, in fubftance 
before it becomes material and perceptible by the fenfes, that 
is to fay, in atomic fubftances. Individualities mutually ex- 
clude each other. 

The next categoiy ftands as it were by itfelf, and forms the 
top of the pyramidal arrangement of the categories, which 
tapers from the fundamental three, to the qualifying two, and 
ends in that which we tranflate by * Concretion. ' It is pecu- 
liar to Indian philofophy and difficult to be rendered into the 
philofophical language of Europe. It expreffes the intimate 
relation of things which cannot exift feparately. A quality, 
for inftance, cannot exift by itfelf, but only as the quality of a 
fubftance, nor can fubftance exift except with reference to qua- 
lities. Now, fubftance and quality are notconfidered as merely 
together, but as interwoven, as infeparable, and mutually de- 
pendent ; and this relation is exprelfed by the category of 
Concretion. The fame relation exifts between the whole and 
its parts, between Genus and Species, between caufe and effect. 
The laft categoiy, which, as we faw, is omitted by fome of 
the Vaifefhikas, is that of Non-exiftence. It is of four kinds, 
according as it applies to things: i. Which are not yet, but 
maybe afterwards ; 2. Which are no more, but have been 5 
3. Which are not, and never will be 5 4.. Which are not what 
fomething elfe is, i. e. which differ. 

Of thefe feven categories, which exhauft the univerfe of 
knowledge (omne fcibile), Subftance comprehends the five 
elements, earth, water, light, air and ether, time and fpace ; 
foul and felf. The five elements may be either eternal, un- 
created, not perceptible by the fenfes, but eftablifhed by infer- 
ence $ or created, perceptible and deftruc~Hble. In the former 
ftate they exift as infinitely fmall, in the latter they are pro- 
duels. Confidered as products again, the elementary fub- 
ftances are threefold ; organic, organ, or inorganic* Earth, 
which is determined as that which has the quality of Odour, 
exifts, as organic, in animal bodies. As organ it is the appre- 
hender of odour, as inorganic it exifts in ftones. In this man- 



376 A PP END IX. 

ner we get five organs : the organ of hearing correfponding to 
the fubftance of ether ; that of feeling to the fubftance of air 5 
that of feeing to light ; that of tafting to water; that of fmell- 
ing to earth. Ether has one quality, and the organ of hear- 
ing apprehends one quality, that of found. Air has two 
qualities, and the organ of feeling apprehends two, thofe of 
found and tangibility. Light has three qualities, and the 
organ of fight apprehends three, thofe of found, tangibility, 
and colour. Water has four qualities, and the organ of tafte 
apprehends four, thofe of found, tangibility, colour, and favour. 
Earth has five qualities, and the organ of fmell apprehends 
five, thofe of found, tangibility, colour, favour, and odour. 
Here then we have the doctrine of Empedocles, 

Tain fxh yap ycuav hie con a [/.zv, v^ari $* uboop 9 
AlBzpi $ alQzpa S'Tov, arap irvpl TCvp afenXov, 
2?opyhv $k cnropyn, vzmoq $z tz vzikzi' Xvypy, 

only carried out to too great an extent, and thereby carica- 
tured. The only remark which it is neceffary to make, is 
that ' ether' is treated differently from the other elements. 
While the other four elements exift both in an atomic and in 
a terreftrial ftate, ether never leaves its tranfcendental reality, 
but is eternal, one, and infinitely great (all-pervading). 

The next two fubftances, which are like ether, eternal only, 
one and all-pervading, are Time and Space, Time is the 
caufe of what we call Paft, Prefent, and Future. Space is' the 
caufe of what we call Eaft, Weft, North, South, etc. Both 
time and fpace being eternal fubftances, and eternal only, it 
follows that they are never perceptible by the organs of the 
fenfes. 

The eighth fubftance is Self. It is the fubftratum of the 
qualities of knowledge, wifh and will. It is twofold, the liv- 
ing Self and the Supreme Self. The Supreme Self is the Lord, 
the Omnifcient ; he is One only, free from joy and forrow. 
The living Self is attached to different bodies, but it is ftill 
eternal and all-pervading. Wherever the body is, there is the 



ON INDIAN LOGIC. 377 

living Self 5 but even the living Self remains uncreated and 
eternal. Its exiftence can be proved, but it cannot fall under 
the cognition of the fenfes. The laft fuhftance is foul, the 
caufe of perception, of pleafure and pain, and the paflions. 
As Self, though attached to bodies, is all-pervading and in- 
finitely great, it would not be fufficient to account for the fact 
of our fucceffive knowledge. We mould, like the Omnifcient, 
know everything at once, unlefs there was the foul, through 
which all impreffions pafs in fucceflion and become individual- 
ized. Soul, too, is eternal only, but it is endlefs, not infinitely 
great, but infinitely fmall, and attached not to the Supreme, 
but to living Selves only. 

It is not neceffary to enter into a more detailed account of 
the fubftances, for it is clear that there is only one Subftance 
which will fail under our more immediate consideration, the 
Subftance of Self, and this only as the fubftratum of the qua- 
lity of knowledge. It is where the quality of knowledge is 
examined, that we fhall recognize what by European philofo- 
phers is treated as Logic. 

Before we proceed to that Chapter, we fhall only give the 
different headings of the two categories of quality and action. 

Qualities are, i. Colour ; 2. Savour ; 3. Odour; 4. Tangi- 
bility ; 5. Number; 6. Dimenfion ; 7. Diftinction ; 8. Con- 
junction; 9. Disjunction ; 10. Priority; 11. Pofteriority : 
12. Weight; 13. Fluidity; 14. Vifcidity ; 15. Sound; 16. 
Perception 5 17. Pleafure; 18. Pain; 19. Defire; 20. Aver- 
fion ; 21. Effort; 22. Merit; 23. Demerit; 24- Faculty. 
They are eternal if refiding in eternal fubftances, and non- 
eternal if refiding in material bodies. Knowledge, Pleafure, 
and Pain, Defire and Averfion, Effort, Merit and Demerit, 
are qualities of the Self only. Perception, Defire, and Effort, 
are eternal as qualities of the Supreme Self, but non-eternal as 
qualities of living Selves. Actions are, Lifting up, Throwing 
down, Contraction, Expanfion, and Proceflion. They exift 
only in the four elements and in Soul. 

The fourth Category, or Genus, is fomething which refides 
in fubftance, qualities and actions, but is eternal, and as fuch 



378 APPENDIX. 

not fenfuoufly perceptible. It is one, but it always refides in 
many. It is that by which it becomes pofiible to comprehend 
feveral things into one clafs, and to predicate fomething of 
them, which they have in common* We call this an abftrac- 
tion, but to the Hindu the Genus of things or the General, 
is fomething real, inherent in fubftance, or quality, or action, 
though of courfe not material or perceptible by the fenfes. 
The Genus, therefore, or the caufe of what we call general, 
though it can be conceived as independent of fingle objects, is 
known to us only as inherent in the objects of intuition. It 
is inherent in fubflances, qualities, and actions, and is per- 
ceived by us as we perceive either fubflances, actions, or qua- 
lities. But what Kanada means by calling Genus inherent, 
is that fubftances, qualities, and actions cannot exift, not even 
in their eternal ftate, without the Genus. The fame applies 
to Individualities, only that they do not inhere in qualities and 
actions, but in fubftances only. Individuality is what makes 
a thing to be itfelf, and not anything elfe. And if we hear 
Kanada exprefling his opinion that ' individualities which 
mutually exclude one another, exift in fubftances only,' we are 
ftrongly reminded of Ariftotle's tenet, to t( Icrrtv airXZg rn ola-ta, 

Thefe five categories would apparently exhauft the meaning 
of every word (padartha). If we take, for inftance, the word 
lightning, and afk Kanada what is exprefled by it, he 
would fay, firft a fubftance, and more particularly, an ele- 
mentary fubftance. Secondly, a number of qualities, like co- 
lour, diftance, or dimenfion. Thirdly, action, and here the 
action of throwing down, which cannot be a quality, be- 
caufe qualities are always conceived as at reft. Fourthly, a 
genus ; becaufe, when we fpeak of lightning, we imply that 
it exifts not once only, but as a clafs, which clafs is a lower 
genus if compared with light. Fifthly, an individuality, be- 
caufe we mean this particular lightning, which never exifted 
before and never will exift again. Neverthelefs, fays Kanada, 
thefe five categories do not yet contain all that we mean by the 
word lightning. It is not the mere agglomerate of fubftance, 



ON INDIAN LOGIC. 379 

quality, etc. that conftitutes a real conception — but thefe cata- 
gories rauft again be intimately connected or interwoven, be- 
fore they reprefent or conftitute a reality. The juxta-pofition 
of categories would be a mere abftraction, and it requires the 
category of concretion to make it concrete and real. With 
it, we predicate, not, firft fubftance, then quality, and fo on, 
but we predicate fubftance as neceflitating quality, quality as 
infeparable from fubftance, genus inherent in both, and indi- 
viduality fupported by genus. Thus only does a real concep- 
tion become fully exhaufted by categorical analyfis. 

We now return to a confideration of the qualities, and more 
efpecially of that which is called " Knowledge. " Knowledge 
is a quality of the Self in the fame manner as colour is of light. 
It is infeparably connected with it, and is explained as the 
caufe of every conception that is expreffed in language. Know- 
ledge is either remembrance or perception. Perception is two- 
fold, right or wrong. Right perception reprefents the thing 
fuch as it is, fdver as filver. This is called truth (prama). 
Wrong perception reprefents the thing as the thing is not, 
mother-o , -pearl as fdver. 

Right perception is fourfold, fenfuous, conclufive, compara- 
tive, and authoritative. It is produced by the fenfes, by infer- 
ring, by comparing, and by revealed authority. This fourfold 
divifion of knowledge is taken from Gotama and not from 
Kanada. Kanada admits but two fources of knowledge, per- 
ception (pratyakfha) and inference (laingika), that is to fay, 
he comprehends all knowledge which does not arife from the 
fenfes, under the general title of inference. The different fyf- 
tems of Hindu philofophy have been arranged by Colebrooke, 
according to what each confiders to be the only truftworthy 
means of knowledge. The Carvaka or Materialift admits but 
one "fource of knowledge, fenfuous perception. The Bud- 
dhift and the Vaifeihika admit two, perception and inference. 
Manu (xii. 105,) and Sankhya philofophers admit three, for 
they acknowledge, befides perception and inference, the autho- 
rity of revelation. The followers of Gotama add comparifon 



380 APPENDIX. 

as a fourth inftrument of knowledge ; the Prabhakaras pre- 
fumption as a fifth, and the Mimaniakas privation as a fixth. 
To the Self it is indifferent whether its knowledge is produced 
by any one of thefe inflruments, as long as each reprefents the 
thing fuch as it is. 

We pais over the chapter on caufation, which ferves as an 
introduction to the chapter on fenfuous perception. Nor do 
we enter into the intricacies of fenfuous perception, of which 
fix different kinds are enumerated and explained. They arife 
from the different ways in which the organs of fenfe are 
brought into contact with their objects, which objects may be 
either fubftantial matter, or qualities and actions, as inherent 
in fubftance, or the Genus, as inherent in fubftances, qualities, 
and actions. 

After fenfuous knowledge comes conclufive knowledge, 
which is gained by means of inferring. Conclufive know- 
ledge is, for inftance, c This mountain is a volcano, 1 though our 
fenfuous perception is only that the mountain fmokes. In 
order to arrive from this at the conclufion, that it is a volcano, 
we muft be in poffeflion of what is called a pervading rule or 
Vyapti. This pervading rule, which fometimes might be 
called a law, is, that fmoke is infeparably conne6i:ed with fire, 
or as the Hindu calls it, that fmokinefs is pervaded by fieri- 
nefs, that wherever there is fmoke there is fire. If we poffefs 
this Vyapti, which we may remember by fuch inftances, as 
a culinary hearth, etc., then, in order to arrive at conclufive 
knowledge, we only require confideration (paramarfa), in 
order to find out in any fenfuous impreffion fomething which 
can be pervaded, fomething which can make the mountain the 
member (pakfha) of a Vyapti, this being, in our cafe, the 
fmoke. If we know that the fmoke, which we perceive, is 
qualified to become part of a Vyapti, (this Vyapti being, where- 
ever there is fmoke, there is fire), then we know conclufively 
that this mountain is fiery, becaufe it fmokes. 

It would have been eafy to tranflate thefe definitions into 
more technical language. We might have clothed Kanada 



ON INDIAN LOGIC. 381 

in a Grecian garb, and made him look almoft like Ariftotle. 
Inftead of faying, that conclufive knowledge arifes from a 
consideration that there is fomething in an object which is 
pervaded by fomething elfe, and that the pervading predicate 
is predicable of all things of which the pervaded predicate is, 
we might have faid, the conclufive knowledge that S is P, 
arifes from the confideration that S is M, and M is P, or with 
Anftotle cruXXoynTf^og ha, rov fxitrov to aKpv nrta rpiTa &EiKW<7iv. 
What Kanada calls member of a pervalion (pakfha, e. g. moun- 
tain), we might have tranflated by fubject or terminus minor; 
what pervades (vyapaka or fadhya, e. g. fierinefs), the predi- 
cate or terminus major; and what is to be pervaded (vyapya, 
e. g. fmokinefs), the terminus medius. But what mould we 
have gained by this ? All that is peculiar to Indian philo- 
fophy would have been eliminated, and what remains would 
have looked like a clumfy imitation of Ariftotle. Multa fiunt 
eadem fed aliter, and it is this ' aliter' which conftitutes the 
principal intereft in a comparative ftudy of philofophy. Even 
fuch terms as conclufion or fyliogifm are inconvenient here, be- 
caufe they have with us an hiftorical colouring, and throw a falfe 
light on the fubjecl. The Sanlkrit anumana is not a-vfxir^aa-^a., 
but it means ' meafuring fomething according to fomething 
elfe.' This is done by means of ' paramarfa, which means 
c groping,' or trying to find in an object fomething which can 
be meafured by fomething elfe, or which can become the 
member of a pervafion. This correfponds to the diicovery of 
a terminus medius. In Kapila's fyftem (I. 61), the prin- 
cipal object of inference is faid to be tranfcendental truth. 
Things which cannot be feen with our eyes, are perceived by 
inference, as fire is from fmoke, and he defines inference (I, 
1 01,) by ' knowledge of the connected, arifmgfrom perception 
of a connection or a law.' But, again, the relation of what 
pervades and what is pervaded is very different from what we 
mould call the relative extenfion of two conceptions. This 
will become more evident by what follows. For the prefent 
we have learnt, that the act of proving (anumana) confifts 



382 APPENDIX. 

in our knowing that there is on the mountain fire-pervaded 
fmoke. Through this we arrive at anumiti or conclufive 
knowledge, that the mountain is a volcano. 

What follows is tranflated from Annambhatta's Compen- 
dium. 'The aft of concluding is twofold, it being intended 
either for one's own benefit or for others.'' The former is the 
means of arriving for onefelf at conclufive knowledge, and 
the procefs is this. By repeated obfervation, as in the cafe of 
culinary hearths and the like, we have obtained the general 
rule (vyapti), that wherever there is fmoke there is fire. We 
now approach a mountain, and wonder whether there might 
not be fire in it. We fee the fmoke, remember the general 
rule, and immediately perceive that the mountain poffeffes fire- 
pervaded fmoke. This is, as yet, called only groping after 
figns (lingaparamarfa). But from it arifes the conclufive 
knowledge, that the mountain itfelf is fiery. This is the 
actual procefs when we reafon with ourfelves.' 

6 If we try, however, to convince fomebody elfe of what we 
know to be conclufively true, then we itart with the affertion 
The mountain is fiery. Why ? Becaufe it fmokes 5 and all 
that fmokes, as you may fee in a culinary hearth and the like, 
is fiery. Now you perceive that the mountain does fmoke, 
and hence you will admit that I was right in faying, that the 
mountain is fiery. This is called the five-membered form of 
expofition, and the five members arefeverally called, 1. AfTer- 
tion, the mountain has fire; 2. Reafon becaufe it has fmoke; 
3. Propofition, all that has fmoke, has fire ; 4. Affumption, 
and the mountain has fmoke ; 5. Deduction, therefore it 
has fire. The means of inference in both cafes is the fame. 
It is what was called the groping after figns, or the handling 
of the demonftrative tokens, in which the procefs of inferring 
confifts.' 

Wh^it is called by Annambhatta the conclufion for one felf 
correfponds totidem verbis with the firfl form of Ariitotle's 

fyllogifm. 

All that fmokes is fiery, 
The mountain fmokes ; 
Therefore the mountain is fiery. 



ON INDIAN LOGIC. 383 

What is called the conclufion for others feems more irregular, 
on account of its five members, and of the additional inftances, 
which feem to vitiate the fyllogifm. 

We muft not forget, however, that whatever there is of 
Logic in thefe fhort extracts, has but one object, that of de- 
fcribing knowledge as one of the qualities of the Self. Know- 
ledge is not confined to fenfuous perceptions, and therefore 
knowledge gained by inference is examined next. The ques- 
tion is, how is it that we know anything beyond what we 
perceive with our fenfes ? The anfwer is, by inferring. If 
we place ourfelves on this point of view, which Kanada has 
taken, it becomes clear, firft, that we cannot expect from Ka- 
nada a treatife on formal Logic. The formal Logician takes 
a purely Scientific intereft in the machinery of the human 
mind. He collects, arranges, and analyfes the functions of 
our reafoning faculties, as they fall under his obfervation. 
But the queftion which occupies Kanada is, how is it that we 
know things which we do not fee, and how can we prove that 
we do know them ? Now the inftrument by which we know 
things which we do not perceive with our fenfes, is inference. 
Hence, Kanada has to explain firft, what inference is, and 
how we do infer ; fecondly, how far inference can be made 
to yield the fame certainty as our fenfuous impreffions. For 
this purpofe, it feems that neither the deductive nor the induc- 
tive fyllogifm, if taken by itfelf, would have been fiifncient. 
Deductive reafoning may in itfelf be moft valuable for formal- 
izing facts, it may give a variety of different afpedts to our 
knowledge, but our knowledge will never be fubftantially in- 
creafed, no new fact will ever be difcovered by it. And if on 
one fide Kanada cannot ufe deduction becaufe it teaches no- 
thing new, he cannot ufe induction either, at leaft not in its 
general acceptation, becaufe it teaches nothing certain. 

The only object of all knowledge with Kanada, as we faw 
before, was abfolute truth, or prama. Now Ariftotie does not 
make a fecret of it, that the inayooyh, in order to prove the 
o\»s, muft be ha navrcav. and that this is impoffible. Know- 



384 APPENDIX. 

ledge gained by epagogic reafoning is, ftri&ly fpeaking, 
always \ici to ttoXv, not what Kanada would call prama. 
The conclufion which Ariftotle gains by way of induction, 
c Animals which have little bile are long-lived', might be 
called a Vyapti. Ariftotle arrives at this, by faying, man, 
horfe, and mule (C) are long-lived (A), man, horfe, and mule 
(C) have little bile (B), therefore all animals with little bile 
are long-lived. But Kanada would exprefs himfelf in a differ- 
ent way. He would fay, wherever we perceive the attribute 
of little bile, we alfo perceive the attribute of long life, as, for 
inftance, in men, horfes, mules, etc. But here he would not 
ftop, but he would value this vyapti merely as a means for 
eftablifhing a new fa6t ; he would at once ufe it as a means 
of deduction, and fay, ' now the elephant has little bile, there- 
fore is he long-lived. 

One thing can be faid in favour of the Indian method. If 
we go on accumulating inftances, as in the cafe before-men- 
tioned, if we add horfes, mules, men, and the like, we ap- 
proximate more and more towards a general rule, but we do 
never eliminate real exceptions, not to fpeak of poflible excep- 
tions. The Hindu, on the contrary, by faying, ' Wherever 
we fee the attribute of little bile, we obferve long life, and 
then giving a number of inftances by way of illuftration, ex- 
cludes the reality, though he does not exclude the poflibility, of 
exceptions. He ftates it as a facl, that wherever the one has 
been, there has been the other, which throws the onus probandi 
as to a cafe to the contrary, upon the other fide. In our fyf- 
tem, there is nothing to force an opponent to admit a hun- 
dredth cafe, becaufe in ninety-nine cafes the rule happened to 
be true — while, if it is impoflible to attack the ' Wherever' of 
the Hindu, there is in this Wherever a real power that brings 
conviction for every cafe that comes under it. If it can be 
proved that there never was an inftance where fmoke was 
feen without fire, the mutual inherence and infeparable con- 
nection of fmoke and fire is eftablifhed more ftringently than 
by any number of accumulated inftances where the two have 



ON INDIAN LOGIC. 385 

been feen together. The conditions under which it is allowed 
to form a Vyapti, that is to fay, to form Univerfals, have oc- 
cupied the attention of Hindu philofophers more than any 
other point in Logic. They diftinclly exclude the mere ac- 
cumulation of obfervations. For things, they fay, may be 
together a hundred times, and may Mill not be mutually inhe- 
rent. They make exceptions for practical purpofes, when 
repeated obfervations may be turned into a general rule, but 
not in philofophical difcuffions. Volumes after volumes have 
been written on this fubje6t, and though I do not believe they 
will throw new light on the queftion of the origin of Univer- 
fals, yet they would furnifh a curious parallel to the hiftory of 
the European Intellect. 

It will be neceffary, before clofing thefe remarks, to fay a 
few words in anfwer to the attacks which have been made on 
Indian Logic. 

It has been faid that the inftances which occur in the third 
member of the five-membered argument, vitiate the conclufion. 
The proportion that wherever there is fmoke there is fire, was 
fuppofed to lofe its univerfal character if it was followed by an 
inftance, 'as in the culinary hearth.' Againft this we have to 
remark, firft, that this inftance is not effential and is therefore 
occafionally left out altogether. Next, the inftance is never 
ufed to confirm the univerfal proportion, but to illuftrate it, 
and in this refpecl: it is of particular ufe in rhetorical induc- 
tions. From the Sutras of Gotama (I, 35), it might certainly 
appear, as if the third member had nothing to do but to give 
an inftance. He fays, " the proportion is an inftance which 
from the fac~l that fmoke accompanies fire, fhows that fire 
muft be there.'"' However, the Commentator explains that 
this is not ftriclly a definition of the third member, but merely 
an explanation. What the third member fupplies is a ftatement 
that fierinefs pervades fmokinefs, together with an example to 
make the connection between them more evident. 

In the original work of Kanada, of which the Libraiy of 
the Eaft India Houfe poffeffes a MS., containing text and 

c c 



386 APPENDIX. 

commentary, we fee ftill more clearly that the third member is 
fimply an univerfal propofition. We read there (p. 76, a.), 
" Inference is twofold, either for onefelf or for others. That 
for others confifts of five fentences, which are called Affertion, 
Reafon, Propofition, Affumption, and Deduction. AfTertion 
does not mean more or lefs than the wording of the conclufive 
knowledge which is to be eftablifhed. Reafon is that member 
which expreffes in the ablative the means of proof. Propofi- 
tion is the third member, which mows that the means of proof 
and what has to be proved by it, are never one without the 
other. The Affumption fhows that the means of proof (here- 
tofore determined as infeparable from what is to be proved) 
belongs to the fubjecl of our affertion. And the Deduction 
fhows that therefore what is to be proved alfo belongs to the 
fubjecl. The argument therefore proceeds in the following 
way. A word is non-eternal ; becaufe it is compofed ; what- 
ever is compofed is non-eternal 5 a word poffeffes the quality 
of being compofed, fuch quality being pervaded by non-eter- 
nity j therefore a word is non-eternal.' He further ftates that 
the names of the five members mean with the Vaifefhikas, 
Promife, Pretext, Authority, Scrutiny, and Repetition. 

In Kanada's fyftem, therefore, it would feem as if the in- 
ftance, belonging to the propofition, was altogether ignored, 
and we might feel inclined to admit that it occurs only inci- 
dentally in Gotama's philofophy. But if we enquire more 
carefully, we find that the inftance in Gotama's fyllogifm has 
a diftincl: office, not to ftrengthen or to limit the univerfal 
propofition, but to indicate, if I may fay fo, its modality. 
Every Vyapti muft, of courfe, admit at leaft one inftance. Thefe 
inftances may be either pofitive only, or negative only, or both 
pofitive and negative. If it is faid, c The jar is nameable, 
becaufe it is knowable 5 everything that is knowable is name- 
able ;' we can only have pofitive inftances, as tree, table, and 
the like. It is impoflible to bring a negative inftance, of 
fomething which is not provable, becaufe everything is prov- 
able. On the contrary, if we have a cafe, like * the earth is 



ON INDIAN LOGIC. 387 

different from all the other four elements, becaufe it has 
odour,' it is impoflible to go on — * All that is different from 
the other elements, has odour, 1 — becaufe the only cafe in point 
would again be ( earth.' Therefore we muft here employ the 
negative Vyapti, and fay, Whatever is not different from the 
other elements, has no odour, and then it is poflible to add an 
inftance, namely, water, light, &c. After this the Hindu pro- 
ceeds, Now earth is not fo (not inodorous ;) Therefore it is 
not fo (not different from the other elements). 

Brahmans have been told by European Logicians that they 
could have all this more cheaply, by faying, ' Whatever is 
odorous differs from the other inodorous elements f ' Earth is 
odorous 5' ' Therefore earth differs from the others :' But the 
Vaifefhika flops us at the very firft word, he does not admit the 
' Whatever,' becaufe it is not a c Whatever,' but only one 
fingle cafe. It would be impoflible to give inftances, nay, to 
give a fingle inftance to the Vyapti, propofed by the European 
Logicians, except earth over again. 

The third cafe is, where the Vyapti admits both of pofitive 
and negative inftances, as in the hackneyed fyllogifm of the 
volcano. Here we can fay, Wherever there is fmoke, there 
is fire, as in culinary hearths and the like. And wherever 
there is no fire there is no fmoke, as in the lake. 

So much for the inftances added to the third member, which 
were fuppofed to vitiate the fyllogifm. 

Still more unfounded is another objection. It was faid that 
the formalities of the Science of Logic were perfectly fatisfied 
with three out of the five members of the Indian fyllogifm. 
Of courfe they are, and the Hindus knew this 2000 years 
ago. We have feen that the five-membered method was 
employed when a perfon, after having himfelf arrived at con- 
clufive knowledge, wifhed to perfuade fomebody elfe of the 
truth of his belief. Now, if ' the fole objecl of Logic is the 
guidance of our own thoughts, and the communication of 
thofe to others is under the confideration of Rhetoric,' it is 
clear that the fcheme of the five-membered fyllogifm belongs 



388 APPENDIX. 

to Rhetoric and not to Logic. Whether or no the five fteps 
as they follow one another, according to Kanada, reprefent 
what does actually take place in a well condu6ted argument, 
we may leave to Rhetoricians to decide. But, in order to 
mow that even this far-fetched objection would not take the 
Brahman philofopher by furprife, we quote the following paf- 
fage from the Vedanta-paribhafha : ' Inference is two-fold, in- 
tended either for ourfelves or for others. The former has 
been explained. As to the latter, it is to be accomplifhed by 
means of an argument. An argument confifts of feveral mem- 
bers. And real members there are only three; affertion, 
reafon, proportion ; or propofition, affumption, and deduction. 
Not five 3 for thefe are fufficient to exhibit the pervading rule 
and its two members, the other two can therefore be difpenfed 
with.' Now, in the firft cafe, which would give us ' the 
mountain is fiery, for it fmokes, all that fmokes is fiery,' it 
muft be admitted there -would be a want of all fyllogiftic ar- 
rangement. The firft two members might be called an En- 
thymema, but then the third would be fuperfluous. But the 
fact is that Hindu philofophers never ufe the three members in 
this fucceflion; and if they fay, that the three firft are fuffi- 
cient for a conclufion, they do not take account of their fuc- 
ceffive collocation, but fimpiy mean that Propofition, Reafon, 
and Affertion would form a fyllogifm as well as Propofition, 
Affumption, and Deduction. But, although the Hindu Lo- 
gicians admit, in common with their brethren in Europe, that 
a complete fyllogifm confifts of three members, they do by no 
means reftrict themfelves to the ufe of the three-membered 
fyllogifm. Gotama, for inftance, fays there are three kinds of 
fyllogifm, from caufe to effect, from effect to caufe, and from 
the Special to the General. Thus we infer that it will rain 
from the rifing of clouds, it has rained from the riling of 
rivers ; we infer that a thing is fubftance becaufe it is earth. 
But, with the exception of the laft cafe, it would be impofTible 
to frame an abfolute propofition, or a vyapti, from which the 
deductions could be eftablifhed. 



ON INDIAN LOGIC. 389 

So much in anfwer to objections which have repeatedly been 
made agamft Indian Logic. I mould like to fee theBrahmans 
themfelves take up the gauntlet and defend their Logic againft 
the attacks of European critics. Till very lately they enter- 
tained a very low opinion of European Logic, fome account of 
which had been fupplied to them from the popular work of 
Abercrombie. Our ftyle is to them not fufficiently precife. 
The ufe of an abftra6t, inftead of a concrete term is enough to 
difguft a Brahman. Befides, he wants to fee all refults put 
forward in fhort and clear language, and to have all pofTible 
objections carefully weighed and refuted. By the exertions of 
Dr. Ballantyne, the Principal of the Sanfkrit College at Be- 
nares, fome of the beft Englifh works on Logic have been 
made accefBble to the Pandits, and at the prefent day we 
might hear the merits of Bacon's Novum Organon difcufTed 
in the ftreets of Benares. Indian Philofophy therefore ought 
not to be attacked at random. Thales, or Empedocles can 
be criticifed in the fchools with impunity, but Kanada and 
Gotama may find champions in India, and perhaps even in 
Europe. 



INDEX. 




POSTERIORI, 62 

A priori, 62 5 changes 

in meaning of, 68 
Abstraction, 98 j fteps 
of, 99 

Accident, 151; and genus, con- 
fufed, 152 

Affinity, chemical, 305 

Alexander, 280 

Alkalies, 309 

All, ambiguous, 172 

Ampere, M. A. M., 361 

Analogy, 3275 in ufe of names, 
328 5 canon of, 328 5 and In- 
duction, 330 

Analyiis and fynthefis, 311 

Analytic of Ariftotle, 72 

Analytic judgments, 185 

Anticipation, 299 

Applied Logic, 275 

Applied Logic, fphere of, 7 

Architectonic, 68 

Argument, diffolution of an, 351 

Ariftotle, 132, note j 177, 181, 
189, 191, 197, 201, 202,204, 
206, 224, 226, 279, 280, 284, 
316,321, 324,325, 352, 355, 
357> 359 5 on Ethics, 353; on 
Science and Art, 13 3 on Form 
and Matter, 24, 30 5 on Nouns 
and Verbs, 48 5 on Plato, 

Arithmetic, Moral, 339 



Arnauld, 273 

Art, the practice of, implies un- 

confcioufnefs, 16 
Art and Science, 13 
Aftronomy, ancient, 302 
Attribute, the predicable, 158 
Attributes, 102 
Averages, 349 
Averroes, 231 
Axiom, 355 

Bacon, 134, 301 

Bayes' Rule, 339 

Baynes, Mr. T e S. 245, 2^9 

Belief, 314 

Berzelius, 290 

Boethius, 201, 204 

Buffon, 336, 340 

Buridanus, 342 

Butler, Bifhop, 330 

Canon, Logic a, 72 
Carpenter, Dr. 242 
Categories, 3565 new table of, 

358 ; Indian — Appendix. 
Categories and parts of Speech, 50 
Categorical judgment, 158 
Caufa effendi et cognofcendi, 258 
Caufation, 255 ; Locke on, 255 ; 

Hume, 2565 Leibniz, 256; 

Kant, 256; Maine de Biran 

on, 257 5 Sir W.Hamilton on 

257 



39 2 



INDEX. 



Caufes, 287 ; afibciated, 288 
Caufe, characters of a, 290 
Chance, how far an element of 

art, 17 5 chance, 3315 tried by 

experiment, 335 
Cicero, 283, 326 
Circumftantial evidence, 324 
ClarTification, fyllogifms of, 343 
Cognitions, 93 
Coleridge, (S. T.) 96 
Colligation, 156, 304, 306 
Communicant fpecies, no 
Comparifon, 99 
Complexio, 192 
Compofition, 1^6 
Comte, a Nominalift, 134 
Conceptions, 96 ; higher and 

lower, 99 j formation of, 97 ; 

inference by complex, 209 j 

queftions about, 135 
Concomitant variations, 290 ; 

conditional fyllogifms, 252 
Connexio, 192 
Contrary oppofition, 198 
Contradictory oppofition, 197 
Contradiction, principle of, 279 
Converfion, 202 

Converfio per accidens, 203, 204 
Cornutus fyllogifmus, 270 
Corollary, 355 
Criterion of truth, 277 
Crocodilinus fyllogifmus, 270 
Cruiius, C. A. 280 

Davy, Sir H. 295 

Deduction, 277, 278 

Deduction and Induction, table of 

names of, 313 
Definition, 277, 278, 305, 352; 

related to divifion, 3545 as a 

predicable, 149, 153; fources 

of, 155 5 table of, 157 
Definition and Property, not dif- 

tinguifhable logically, 150 
De Morgan, ProfefTor, 108, 168, 

206, 331, 336 



Denomination, 108 

Defcartes, 278 

Determination, 106 

Determinants, added, 209 

Dialectic of Ariftotle, 72 

Dictum de omni et nullo, 226 5 
de diverfo, 227 j de exemplo, 
228 

Difference, 1475 method of, 290 

Dilemma, 266 ; popular notion 
of, 269 

Diogenes Laertius, 326 

Disjunctive judgment, 159 ; 
viewed as categorical, 167 ; 
inference from, 2125 fyllo- 
gifms, 259 

Distribute, meaning of, 146 

Distribution in judgments, 171 

Divifion, Logical, 109, 156, 277, 
2 7^j 35 2 5 related to defini- 
tion, 354; fum of the mem- 
bers in, in 

Donkin, ProfefTor, 331 

Downes, Mr. G. O. 331 

Drobifch, in, 251 

'Eikoc;, 321 

Elenchus, 352 

Enthymeme, 270 ; rhetorical, 

321 ; its kinds, 322 ; and ufes, 

323 
Epictetus, 283 
Epifyllogifm, 271 
Eriftic, 72 
Errors, 351 
Euclid, 353 

Euler, 249 ; his notation, 250 
Evidence, 278 5 circumftantial, 

324 
Example, 325 
Excluded Middle, 280 
Experiments, 293 
Explication, 305 
Extenfion and Intenfion, 103 ; 

table of, 104 j modes of ex- 

prefling, 105 



INDEX. 



393 



Extenfion of judgments, 180 

Fallacies, 351 

Figure of Syllogifm, the fourth, 
231 

Figures of fyllogifm, 3 18 ; of fyl- 
logifm, 225 j their fpecial ca- 
nons, 227 5 new fpecial canons, 
230 

Form, three fenfes of, 22 5 and 
matter, 21 5 Plato on, 22, 27, 
note ; Bacon on, 22, 29, note ; 
Coleridge on, 22 j and matter 
may change places, 24, note. 

Fundamentum divifionis, 109 

Galen, 231 

Generalization, 98, 99 

Genus, 100, 147, 1505 fum- 

mum, fubalternum, 100, 101; 

proximate, 102 
Geometry, 3 
Goclenius, 265 
Goethe, 301 
Gotama, 4, 225 
Grammar, univerfal, its province, 

5 2 

Hall, Sir James, 312 

Hamilton, Sir W. 14, 146, 168, 
177,180,185,224, 230, 234, 
245, 247, 257 

Herfchel, Sir J.2 90, 3635 Preli- 
minary Difcourie, recommend- 
ed, 83 

Heuriftic, 72 

Heyder, 284, 326 

Hindu Logic, 4, 369 

Hiftorical records, 349 

Hume, 341, 256 

Hypothecs, 355 

Hypothetical judgment, 1585 five 
forms of, 160 j proper and im- 
proper, 161 5 reduced to cate- 
goricals, 163 



Idea and Law, 22 
Identical proportions, 186 
Identity, principle of, 280 
Imagined reprefentations, their 

place in Logic, 136 
Incontinent oppofition, 199 
Induction, 277, 278 j its name, 
2835 methods of, 2873 by 
fimple enumeration, 261 5 com- 
plete and incomplete, 306 ; ca- 
non of, 307 5 from particulars 
to particulars, 326 5 by imper- 
fect enumeration, 326 
Inductive conception, 304 
Inference, immediate and medi- 
ate, 193 j immediate, from a 
disjunctive judgment, 2125 by 
fum of predicates, 212 j imme- 
diate, 193 ; by oppofition, 195 ; 
by converfion, 202 5 by pri- 
vative conceptions, 2055 by 
added determinants, 209 ; by 
complex conceptions, 209 ; by 
interpretation, 210 j mediate, 
canon of, 214 
Inftance, 351 
Intellect, luggeftive and critical 

powers of, 77 
Inteniion, 1035 of judgments, 
180 j firft and fecond, 30 j Boe- 
thius on, 315 Zabarella, Pa- 
cius, Buhle, Hamilton, Aid- 
rich on, 32 
Interpretation, inferences by, 210 
Intuitions, 96 
Is, ambiguous, 172 

Judgment, denned, 143 ; is of 
thoughts and things, 1445 of 
exiftence, 86 5 modality of, 
3 14 j relation of, 144; an 
equation in, 146 j table of the 
form of, 175; examples of, 
1 7 6 5 have three powers, 1 805 ex- 
plicative and ampliative, 1855 
plurative, 168 5 numerically 



394 



INDEX. 



definite, 1685 affirmative, ne- 
gative, indefinite, 1695 nega- 
tive, controverfy about, 177 j 
categorical, hypothetical, dif- 
junclive, 1585 univerfal, par- 
ticular, lingular, 167 

Kanada, 358, and Appendix 
Kant, 185, 187 5 213, 226, 233, 

256, 2795 on the boundaries 

of Logic, 9 
Keckermann, 31, note, 177, 228 
Kepler, 304 
Kiefewetter, 265 
Krug, 265 

Lambert, 228, 238 

Language defined and divided, 34; 
four functions of, 35 5 analyfes 
thought, 35 5 analytic and iyn- 
thetic, 35, 365 more or lefs 
analytic, 37 ; Greek, Englifh, 
French, 39 ; of Art inferior to 
that of words, 405 records 
thought, 42 5 Trench on 43 ; 
Owen on, 43; abbreviates 
thinking, 45 5 unfpoken, 53 ; 
opinions of its origin, 565 
growth of, 59 

Lange, 249 

Lapis lazuli, 312 

La Place, 294 

Leibniz, 45, no, 206, 209, 226, 
237,256,281,277 j andLocke, 
66 

Lemma, 356 

Locke, 186, 187, 255 5 and Leib- 
niz, 66 

Logic, 319 ; origin of, 3 — 5 ; de- 
fined, 5 5 pure and applied, 7 5 
pure, not concerned with the 
matter of thought, 18 5 con- 
cerned with thought and lan- 
guage, 835 an a priori fcience, 
67 j names of, 68 ; ufes of, 
72 j defective ftudy of, 79 5 



what a treatife on mould con- 
tain, 80 ; fuggeftions on ftudy 
of, 81 ; divifion of, 83, and 
objections to it. 843 applied, 
275 ; Indian, 369 
Logical whole, 105 

Maafs, 251 

Maine de Biran, 257 

Marks, 102 5 contrary and con- 
tradictory, 140 

Maupertuis, 49 

Means and Limits, 348 

Metaphyfical whole, 105 

Method, 87, 277 5 of difference, 
290 j concomitant variations, 
290 

Mill, Mr. J. S. 103, 143, 186, 
194, 288, 330, 363 

Modality, 3145 Ariftotle's view, 
316 j belongs to applied Logic, 
why, 170. 

Modes, table of, 248 j of fyllo- 
gifm, table of, 236 

Moral arithmetic, 339 ; certain- 
ty. 315. 

Muller, Prof. Max, 369 

Mynas, Minoides, 232 

Names, new, 346 

Negative judgments, 177 

Newton, 300 

Nominalifm, moderate, 129 ; 
ultra, 129 5 and realifm, chief- 
ly a difpute about method, 
130; works on, 134 

Notation, mode of, 237 

Noun and verb, 48 and note ; the 
elements of language, 60 

O, converfion of, 205 

Object and fubject, 25, note 

Obfervation, 348 

Oken, 300, 301 

Opposition, inference from, 195 , 

table of, £97 j requifites for, 

202 



INDEX. 



395 



Organon, Logic an, 68 

Paley on Hume, 342 

Plato, 22, 27, in, 131, 132, 
278 ; on fcience and its divi- 
fions, 13; Republic, 353 

Ploucquet, 251 

Poets, their " infpiration," 77, 
78 

Poftulate, 355 

Predicable claiTes, 146 ; Ariftotle 
on, 146 5 two dalles of, 1535 
table of Ariftotle's, 153 

PremifTes, order of, 223 

Prepofitions, 38 

Prefentations, 93 3 clear and ob- 
fcure, 94j confufed and dif- 
tinct, 94 j adequate and inade- 
quate, 945 table of, 95 

Principles, 348 j theological, 
349 j natural, 349 5 mathe- 
matical, 349 5 table of, 350 

Privative conceptions, 107 j in- 
ference by, 205 

Problem, 355 

Property, 149 

Profyllogifm, 271 

Prout, Dr. 291 

Quantity, 167 

Quetelet, M. 331, 336, 338, 349 

Quinctilian, 284 

Ramfay, Mr. G. 361 

Realifm, 129 5 of Plato, 131, 132 

Reductio ad abfurdum, 5 

Reduction, 318 

Reflection, 99 

Reichenbach, Baron von, 347 

Reinhard, 284 

Refidual phenomena, 293 

Refolution, 156 

Rhetoric, 72 

Scaliger, J. C, on Noun and 
verb, 48, note 



Schelling, 359 

Science, 276 ; verified and en- 
larged by experience, 2 ; and 
art, 13 ; can be taught, 17 5 
arrangement of a, 352 5 fubor- 
dinate parts of, 355 5 divifion 
of, 361 

Scholion, 356 

S7]juaov, 321 

Sign, 321 

Some, ambiguous, 173 

Sophiftic, 72 

Sorites, 262; Goclenian form, 
265 ; number of conclufions 
in, 2645 progreflive and re- 
greffive, 265 j hypothetical, 
266 

Sound, caufe of, 292 ; and fenfe, 

Species, infima, 100, 101 

Speech, how far neceflary, 535 
parts of, their origin, 49 

Subaltern oppofition, 200 

Subalternant, 200 

Subalternate, 200 

Subject and object, 25, 65 

Subcontrary oppofition, 201 ; To- 
letus on, 201 

Subdivifion, 112 

Sufficient reafon, 281 

Sum of predicates, inference by, 
212 

Syllogifm defined, 191: parts of 
1925 canon and rules of, 2145 
figures of, 225 5 the unfigured, 
2345 deductive and induc- 
tive, 3175 incomplete, 2705 
of clafiification, 343 ; defec- 
tive, 320 ; disjunctive, 259 ; 
complex, 262 ; equivalent, 
242 ; conditional, 252 
Synthefis and analyfis, 311 
Synthetic judgments, 186 

Taylor on Junius, 323 
Theorem, 355 






39 6 



INDEX. 



Thefis, 355 

Thoughts and things, the anti- 

thefis between, 65 
Traduction, 320 
Trendelenburg, Prof., 284, 357, 

358 

Troxler, 265 

Type, 344 

Water, decompofition of, 295 

Weife, Chr. 251, 361 

Wells, Dr. 285 

Whateley, Archbifhop, 137, 327, 



Whewell, Dr. 301, 303, 304, 

3°5> 34 6 > 3 6l > 3 6 3 

Will, freedom of, illuftrated by 

ufe of numbers, 342 
Wolff, 278 
Words, Ariftotle's arrangement 

of, 50, 52 ; are fymbolical 

conceptions, 45 
Xenophon, 283 
Zabarella, 177 
Zetetic, Logic is, 71 



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